해법
sin3(x)+sin(x)=2sin22(x)
해법
x=2πn,x=π+2πn,x=2π+2πn
+1
도
x=0∘+360∘n,x=180∘+360∘n,x=90∘+360∘n솔루션 단계
sin3(x)+sin(x)=2sin22(x)
대체로 해결
sin3(x)+sin(x)=2sin22(x)
하게: sin(x)=uu3+u=2u22
u3+u=2u22:u=0,u=1
u3+u=2u22
측면 전환2u22=u3+u
u를 왼쪽으로 이동
2u22=u3+u
빼다 u 양쪽에서2u22−u=u3+u−u
단순화2u22−u=u3
2u22−u=u3
u3를 왼쪽으로 이동
2u22−u=u3
빼다 u3 양쪽에서2u22−u−u3=u3−u3
단순화2u22−u−u3=0
2u22−u−u3=0
2u22−u−u3인수 :u(u−1)(2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1)
2u22−u−u3
공통 용어를 추출하다 u:u(2u21−u2−1)
2u22−u3−u
지수 규칙 적용: ab+c=abacu3=u2u=2u21u−u2u−u
공통 용어를 추출하다 u=u(2u21−u2−1)
=u(2u21−u2−1)
2u21−u2−1요인:(u−1)(2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1)
2u21−u2−1
합리적인 근정리를 사용하라
a0=1,an=2
의 나눗셈 a0:1,의 나눗셈 an:1,2
따라서 다음 합리적인 숫자를 확인하십시오:±1,21
11이 표현의 어근입니다, 그러니 잘 생각해보세요 u−1
=(u−1)u−12u21−u2−1u−12u21−u2−1=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1
u−12u21−u2−1
u−12u21−u2−1나누다:u−12u21−u2−1=2u20+u−12u20−u2−1
분자의 선행 계수를 나눕니다 2u21−u2−1
그리고 나눗셈 u−1:u2u21=2u20
몫=2u20u−1 에 2u20로 곱하시오 2u21−2u20 새 나머지를 얻으려면 2u21−u2−1 에서 2u21−2u20빼십시오 나머지=2u20−u2−1
그러므로u−12u21−u2−1=2u20+u−12u20−u2−1
=2u20+u−12u20−u2−1
u−12u20−u2−1나누다:u−12u20−u2−1=2u19+u−12u19−u2−1
분자의 선행 계수를 나눕니다 2u20−u2−1
그리고 나눗셈 u−1:u2u20=2u19
몫=2u19u−1 에 2u19로 곱하시오 2u20−2u19 새 나머지를 얻으려면 2u20−u2−1 에서 2u20−2u19빼십시오 나머지=2u19−u2−1
그러므로u−12u20−u2−1=2u19+u−12u19−u2−1
=2u20+2u19+u−12u19−u2−1
u−12u19−u2−1나누다:u−12u19−u2−1=2u18+u−12u18−u2−1
분자의 선행 계수를 나눕니다 2u19−u2−1
그리고 나눗셈 u−1:u2u19=2u18
몫=2u18u−1 에 2u18로 곱하시오 2u19−2u18 새 나머지를 얻으려면 2u19−u2−1 에서 2u19−2u18빼십시오 나머지=2u18−u2−1
그러므로u−12u19−u2−1=2u18+u−12u18−u2−1
=2u20+2u19+2u18+u−12u18−u2−1
u−12u18−u2−1나누다:u−12u18−u2−1=2u17+u−12u17−u2−1
분자의 선행 계수를 나눕니다 2u18−u2−1
그리고 나눗셈 u−1:u2u18=2u17
몫=2u17u−1 에 2u17로 곱하시오 2u18−2u17 새 나머지를 얻으려면 2u18−u2−1 에서 2u18−2u17빼십시오 나머지=2u17−u2−1
그러므로u−12u18−u2−1=2u17+u−12u17−u2−1
=2u20+2u19+2u18+2u17+u−12u17−u2−1
u−12u17−u2−1나누다:u−12u17−u2−1=2u16+u−12u16−u2−1
분자의 선행 계수를 나눕니다 2u17−u2−1
그리고 나눗셈 u−1:u2u17=2u16
몫=2u16u−1 에 2u16로 곱하시오 2u17−2u16 새 나머지를 얻으려면 2u17−u2−1 에서 2u17−2u16빼십시오 나머지=2u16−u2−1
그러므로u−12u17−u2−1=2u16+u−12u16−u2−1
=2u20+2u19+2u18+2u17+2u16+u−12u16−u2−1
u−12u16−u2−1나누다:u−12u16−u2−1=2u15+u−12u15−u2−1
분자의 선행 계수를 나눕니다 2u16−u2−1
그리고 나눗셈 u−1:u2u16=2u15
몫=2u15u−1 에 2u15로 곱하시오 2u16−2u15 새 나머지를 얻으려면 2u16−u2−1 에서 2u16−2u15빼십시오 나머지=2u15−u2−1
그러므로u−12u16−u2−1=2u15+u−12u15−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+u−12u15−u2−1
u−12u15−u2−1나누다:u−12u15−u2−1=2u14+u−12u14−u2−1
분자의 선행 계수를 나눕니다 2u15−u2−1
그리고 나눗셈 u−1:u2u15=2u14
몫=2u14u−1 에 2u14로 곱하시오 2u15−2u14 새 나머지를 얻으려면 2u15−u2−1 에서 2u15−2u14빼십시오 나머지=2u14−u2−1
그러므로u−12u15−u2−1=2u14+u−12u14−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+u−12u14−u2−1
u−12u14−u2−1나누다:u−12u14−u2−1=2u13+u−12u13−u2−1
분자의 선행 계수를 나눕니다 2u14−u2−1
그리고 나눗셈 u−1:u2u14=2u13
몫=2u13u−1 에 2u13로 곱하시오 2u14−2u13 새 나머지를 얻으려면 2u14−u2−1 에서 2u14−2u13빼십시오 나머지=2u13−u2−1
그러므로u−12u14−u2−1=2u13+u−12u13−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+u−12u13−u2−1
u−12u13−u2−1나누다:u−12u13−u2−1=2u12+u−12u12−u2−1
분자의 선행 계수를 나눕니다 2u13−u2−1
그리고 나눗셈 u−1:u2u13=2u12
몫=2u12u−1 에 2u12로 곱하시오 2u13−2u12 새 나머지를 얻으려면 2u13−u2−1 에서 2u13−2u12빼십시오 나머지=2u12−u2−1
그러므로u−12u13−u2−1=2u12+u−12u12−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+u−12u12−u2−1
u−12u12−u2−1나누다:u−12u12−u2−1=2u11+u−12u11−u2−1
분자의 선행 계수를 나눕니다 2u12−u2−1
그리고 나눗셈 u−1:u2u12=2u11
몫=2u11u−1 에 2u11로 곱하시오 2u12−2u11 새 나머지를 얻으려면 2u12−u2−1 에서 2u12−2u11빼십시오 나머지=2u11−u2−1
그러므로u−12u12−u2−1=2u11+u−12u11−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+u−12u11−u2−1
u−12u11−u2−1나누다:u−12u11−u2−1=2u10+u−12u10−u2−1
분자의 선행 계수를 나눕니다 2u11−u2−1
그리고 나눗셈 u−1:u2u11=2u10
몫=2u10u−1 에 2u10로 곱하시오 2u11−2u10 새 나머지를 얻으려면 2u11−u2−1 에서 2u11−2u10빼십시오 나머지=2u10−u2−1
그러므로u−12u11−u2−1=2u10+u−12u10−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+u−12u10−u2−1
u−12u10−u2−1나누다:u−12u10−u2−1=2u9+u−12u9−u2−1
분자의 선행 계수를 나눕니다 2u10−u2−1
그리고 나눗셈 u−1:u2u10=2u9
몫=2u9u−1 에 2u9로 곱하시오 2u10−2u9 새 나머지를 얻으려면 2u10−u2−1 에서 2u10−2u9빼십시오 나머지=2u9−u2−1
그러므로u−12u10−u2−1=2u9+u−12u9−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+u−12u9−u2−1
u−12u9−u2−1나누다:u−12u9−u2−1=2u8+u−12u8−u2−1
분자의 선행 계수를 나눕니다 2u9−u2−1
그리고 나눗셈 u−1:u2u9=2u8
몫=2u8u−1 에 2u8로 곱하시오 2u9−2u8 새 나머지를 얻으려면 2u9−u2−1 에서 2u9−2u8빼십시오 나머지=2u8−u2−1
그러므로u−12u9−u2−1=2u8+u−12u8−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+u−12u8−u2−1
u−12u8−u2−1나누다:u−12u8−u2−1=2u7+u−12u7−u2−1
분자의 선행 계수를 나눕니다 2u8−u2−1
그리고 나눗셈 u−1:u2u8=2u7
몫=2u7u−1 에 2u7로 곱하시오 2u8−2u7 새 나머지를 얻으려면 2u8−u2−1 에서 2u8−2u7빼십시오 나머지=2u7−u2−1
그러므로u−12u8−u2−1=2u7+u−12u7−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+u−12u7−u2−1
u−12u7−u2−1나누다:u−12u7−u2−1=2u6+u−12u6−u2−1
분자의 선행 계수를 나눕니다 2u7−u2−1
그리고 나눗셈 u−1:u2u7=2u6
몫=2u6u−1 에 2u6로 곱하시오 2u7−2u6 새 나머지를 얻으려면 2u7−u2−1 에서 2u7−2u6빼십시오 나머지=2u6−u2−1
그러므로u−12u7−u2−1=2u6+u−12u6−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+u−12u6−u2−1
u−12u6−u2−1나누다:u−12u6−u2−1=2u5+u−12u5−u2−1
분자의 선행 계수를 나눕니다 2u6−u2−1
그리고 나눗셈 u−1:u2u6=2u5
몫=2u5u−1 에 2u5로 곱하시오 2u6−2u5 새 나머지를 얻으려면 2u6−u2−1 에서 2u6−2u5빼십시오 나머지=2u5−u2−1
그러므로u−12u6−u2−1=2u5+u−12u5−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+u−12u5−u2−1
u−12u5−u2−1나누다:u−12u5−u2−1=2u4+u−12u4−u2−1
분자의 선행 계수를 나눕니다 2u5−u2−1
그리고 나눗셈 u−1:u2u5=2u4
몫=2u4u−1 에 2u4로 곱하시오 2u5−2u4 새 나머지를 얻으려면 2u5−u2−1 에서 2u5−2u4빼십시오 나머지=2u4−u2−1
그러므로u−12u5−u2−1=2u4+u−12u4−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+u−12u4−u2−1
u−12u4−u2−1나누다:u−12u4−u2−1=2u3+u−12u3−u2−1
분자의 선행 계수를 나눕니다 2u4−u2−1
그리고 나눗셈 u−1:u2u4=2u3
몫=2u3u−1 에 2u3로 곱하시오 2u4−2u3 새 나머지를 얻으려면 2u4−u2−1 에서 2u4−2u3빼십시오 나머지=2u3−u2−1
그러므로u−12u4−u2−1=2u3+u−12u3−u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+u−12u3−u2−1
u−12u3−u2−1나누다:u−12u3−u2−1=2u2+u−1u2−1
분자의 선행 계수를 나눕니다 2u3−u2−1
그리고 나눗셈 u−1:u2u3=2u2
몫=2u2u−1 에 2u2로 곱하시오 2u3−2u2 새 나머지를 얻으려면 2u3−u2−1 에서 2u3−2u2빼십시오 나머지=u2−1
그러므로u−12u3−u2−1=2u2+u−1u2−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u−1u2−1
u−1u2−1나누다:u−1u2−1=u+u−1u−1
분자의 선행 계수를 나눕니다 u2−1
그리고 나눗셈 u−1:uu2=u
몫=uu−1 에 u로 곱하시오 u2−u 새 나머지를 얻으려면 u2−1 에서 u2−u빼십시오 나머지=u−1
그러므로u−1u2−1=u+u−1u−1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+u−1u−1
u−1u−1나누다:u−1u−1=1
분자의 선행 계수를 나눕니다 u−1
그리고 나눗셈 u−1:uu=1
몫=1u−1 에 1로 곱하시오 u−1 새 나머지를 얻으려면 u−1 에서 u−1빼십시오 나머지=0
그러므로u−1u−1=1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1
=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1
=(u−1)(2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1)
=u(u−1)(2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1)
u(u−1)(2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1)=0
제로 인자 원리 사용:\4각형이면 ab=0그렇다면 a=0or b=0u=0oru−1=0or2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1=0
u−1=0해결 :u=1
u−1=0
1를 오른쪽으로 이동
u−1=0
더하다 1 양쪽으로u−1+1=0+1
단순화u=1
u=1
2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1=0해결 :솔루션 없음 u∈R
2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1=0
다음을 위한 하나의 솔루션 찾기 2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1=0 뉴턴-랩슨을 이용하여:솔루션 없음 u∈R
2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1=0
뉴턴-랩슨 근사 정의
f(u)=2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1
f′(u)찾다 :40u19+38u18+36u17+34u16+32u15+30u14+28u13+26u12+24u11+22u10+20u9+18u8+16u7+14u6+12u5+10u4+8u3+6u2+4u+1
dud(2u20+2u19+2u18+2u17+2u16+2u15+2u14+2u13+2u12+2u11+2u10+2u9+2u8+2u7+2u6+2u5+2u4+2u3+2u2+u+1)
합계/차이 규칙 적용: (f±g)′=f′±g′=dud(2u20)+dud(2u19)+dud(2u18)+dud(2u17)+dud(2u16)+dud(2u15)+dud(2u14)+dud(2u13)+dud(2u12)+dud(2u11)+dud(2u10)+dud(2u9)+dud(2u8)+dud(2u7)+dud(2u6)+dud(2u5)+dud(2u4)+dud(2u3)+dud(2u2)+dudu+dud(1)
dud(2u20)=40u19
dud(2u20)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u20)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅20u20−1
단순화=40u19
dud(2u19)=38u18
dud(2u19)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u19)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅19u19−1
단순화=38u18
dud(2u18)=36u17
dud(2u18)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u18)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅18u18−1
단순화=36u17
dud(2u17)=34u16
dud(2u17)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u17)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅17u17−1
단순화=34u16
dud(2u16)=32u15
dud(2u16)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u16)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅16u16−1
단순화=32u15
dud(2u15)=30u14
dud(2u15)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u15)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅15u15−1
단순화=30u14
dud(2u14)=28u13
dud(2u14)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u14)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅14u14−1
단순화=28u13
dud(2u13)=26u12
dud(2u13)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u13)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅13u13−1
단순화=26u12
dud(2u12)=24u11
dud(2u12)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u12)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅12u12−1
단순화=24u11
dud(2u11)=22u10
dud(2u11)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u11)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅11u11−1
단순화=22u10
dud(2u10)=20u9
dud(2u10)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u10)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅10u10−1
단순화=20u9
dud(2u9)=18u8
dud(2u9)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u9)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅9u9−1
단순화=18u8
dud(2u8)=16u7
dud(2u8)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u8)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅8u8−1
단순화=16u7
dud(2u7)=14u6
dud(2u7)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u7)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅7u7−1
단순화=14u6
dud(2u6)=12u5
dud(2u6)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u6)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅6u6−1
단순화=12u5
dud(2u5)=10u4
dud(2u5)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u5)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅5u5−1
단순화=10u4
dud(2u4)=8u3
dud(2u4)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u4)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅4u4−1
단순화=8u3
dud(2u3)=6u2
dud(2u3)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u3)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅3u3−1
단순화=6u2
dud(2u2)=4u
dud(2u2)
정수를 빼라: (a⋅f)′=a⋅f′=2dud(u2)
전원 규칙을 적용합니다: dxd(xa)=a⋅xa−1=2⋅2u2−1
단순화=4u
dudu=1
dudu
공통 도함수 적용: dudu=1=1
dud(1)=0
dud(1)
상수의 도함수: dxd(a)=0=0
=40u19+38u18+36u17+34u16+32u15+30u14+28u13+26u12+24u11+22u10+20u9+18u8+16u7+14u6+12u5+10u4+8u3+6u2+4u+1+0
단순화=40u19+38u18+36u17+34u16+32u15+30u14+28u13+26u12+24u11+22u10+20u9+18u8+16u7+14u6+12u5+10u4+8u3+6u2+4u+1
렛 u0=−1계산하다 un+1 까지 Δun+1<0.000001
u1=−0.90476…:Δu1=0.09523…
f(u0)=2(−1)20+2(−1)19+2(−1)18+2(−1)17+2(−1)16+2(−1)15+2(−1)14+2(−1)13+2(−1)12+2(−1)11+2(−1)10+2(−1)9+2(−1)8+2(−1)7+2(−1)6+2(−1)5+2(−1)4+2(−1)3+2(−1)2+(−1)+1=2f′(u0)=40(−1)19+38(−1)18+36(−1)17+34(−1)16+32(−1)15+30(−1)14+28(−1)13+26(−1)12+24(−1)11+22(−1)10+20(−1)9+18(−1)8+16(−1)7+14(−1)6+12(−1)5+10(−1)4+8(−1)3+6(−1)2+4(−1)+1=−21u1=−0.90476…
Δu1=∣−0.90476…−(−1)∣=0.09523…Δu1=0.09523…
u2=−0.58245…:Δu2=0.32230…
f(u1)=2(−0.90476…)20+2(−0.90476…)19+2(−0.90476…)18+2(−0.90476…)17+2(−0.90476…)16+2(−0.90476…)15+2(−0.90476…)14+2(−0.90476…)13+2(−0.90476…)12+2(−0.90476…)11+2(−0.90476…)10+2(−0.90476…)9+2(−0.90476…)8+2(−0.90476…)7+2(−0.90476…)6+2(−0.90476…)5+2(−0.90476…)4+2(−0.90476…)3+2(−0.90476…)2+(−0.90476…)+1=1.08311…f′(u1)=40(−0.90476…)19+38(−0.90476…)18+36(−0.90476…)17+34(−0.90476…)16+32(−0.90476…)15+30(−0.90476…)14+28(−0.90476…)13+26(−0.90476…)12+24(−0.90476…)11+22(−0.90476…)10+20(−0.90476…)9+18(−0.90476…)8+16(−0.90476…)7+14(−0.90476…)6+12(−0.90476…)5+10(−0.90476…)4+8(−0.90476…)3+6(−0.90476…)2+4(−0.90476…)+1=−3.36053…u2=−0.58245…
Δu2=∣−0.58245…−(−0.90476…)∣=0.32230…Δu2=0.32230…
u3=3.61022…:Δu3=4.19268…
f(u2)=2(−0.58245…)20+2(−0.58245…)19+2(−0.58245…)18+2(−0.58245…)17+2(−0.58245…)16+2(−0.58245…)15+2(−0.58245…)14+2(−0.58245…)13+2(−0.58245…)12+2(−0.58245…)11+2(−0.58245…)10+2(−0.58245…)9+2(−0.58245…)8+2(−0.58245…)7+2(−0.58245…)6+2(−0.58245…)5+2(−0.58245…)4+2(−0.58245…)3+2(−0.58245…)2+(−0.58245…)+1=0.84632…f′(u2)=40(−0.58245…)19+38(−0.58245…)18+36(−0.58245…)17+34(−0.58245…)16+32(−0.58245…)15+30(−0.58245…)14+28(−0.58245…)13+26(−0.58245…)12+24(−0.58245…)11+22(−0.58245…)10+20(−0.58245…)9+18(−0.58245…)8+16(−0.58245…)7+14(−0.58245…)6+12(−0.58245…)5+10(−0.58245…)4+8(−0.58245…)3+6(−0.58245…)2+4(−0.58245…)+1=−0.20185…u3=3.61022…
Δu3=∣3.61022…−(−0.58245…)∣=4.19268…Δu3=4.19268…
u4=3.42618…:Δu4=0.18403…
f(u3)=2⋅3.61022…20+2⋅3.61022…19+2⋅3.61022…18+2⋅3.61022…17+2⋅3.61022…16+2⋅3.61022…15+2⋅3.61022…14+2⋅3.61022…13+2⋅3.61022…12+2⋅3.61022…11+2⋅3.61022…10+2⋅3.61022…9+2⋅3.61022…8+2⋅3.61022…7+2⋅3.61022…6+2⋅3.61022…5+2⋅3.61022…4+2⋅3.61022…3+2⋅3.61022…2+3.61022…+1=391356105797.3665f′(u3)=40⋅3.61022…19+38⋅3.61022…18+36⋅3.61022…17+34⋅3.61022…16+32⋅3.61022…15+30⋅3.61022…14+28⋅3.61022…13+26⋅3.61022…12+24⋅3.61022…11+22⋅3.61022…10+20⋅3.61022…9+18⋅3.61022…8+16⋅3.61022…7+14⋅3.61022…6+12⋅3.61022…5+10⋅3.61022…4+8⋅3.61022…3+6⋅3.61022…2+4⋅3.61022…+1=2126512839249.2053u4=3.42618…
Δu4=∣3.42618…−3.61022…∣=0.18403…Δu4=0.18403…
u5=3.25127…:Δu5=0.17491…
f(u4)=2⋅3.42618…20+2⋅3.42618…19+2⋅3.42618…18+2⋅3.42618…17+2⋅3.42618…16+2⋅3.42618…15+2⋅3.42618…14+2⋅3.42618…13+2⋅3.42618…12+2⋅3.42618…11+2⋅3.42618…10+2⋅3.42618…9+2⋅3.42618…8+2⋅3.42618…7+2⋅3.42618…6+2⋅3.42618…5+2⋅3.42618…4+2⋅3.42618…3+2⋅3.42618…2+3.42618…+1=140327262334.09973f′(u4)=40⋅3.42618…19+38⋅3.42618…18+36⋅3.42618…17+34⋅3.42618…16+32⋅3.42618…15+30⋅3.42618…14+28⋅3.42618…13+26⋅3.42618…12+24⋅3.42618…11+22⋅3.42618…10+20⋅3.42618…9+18⋅3.42618…8+16⋅3.42618…7+14⋅3.42618…6+12⋅3.42618…5+10⋅3.42618…4+8⋅3.42618…3+6⋅3.42618…2+4⋅3.42618…+1=802263679492.2867u5=3.25127…
Δu5=∣3.25127…−3.42618…∣=0.17491…Δu5=0.17491…
u6=3.08501…:Δu6=0.16625…
f(u5)=2⋅3.25127…20+2⋅3.25127…19+2⋅3.25127…18+2⋅3.25127…17+2⋅3.25127…16+2⋅3.25127…15+2⋅3.25127…14+2⋅3.25127…13+2⋅3.25127…12+2⋅3.25127…11+2⋅3.25127…10+2⋅3.25127…9+2⋅3.25127…8+2⋅3.25127…7+2⋅3.25127…6+2⋅3.25127…5+2⋅3.25127…4+2⋅3.25127…3+2⋅3.25127…2+3.25127…+1=50318521009.06572f′(u5)=40⋅3.25127…19+38⋅3.25127…18+36⋅3.25127…17+34⋅3.25127…16+32⋅3.25127…15+30⋅3.25127…14+28⋅3.25127…13+26⋅3.25127…12+24⋅3.25127…11+22⋅3.25127…10+20⋅3.25127…9+18⋅3.25127…8+16⋅3.25127…7+14⋅3.25127…6+12⋅3.25127…5+10⋅3.25127…4+8⋅3.25127…3+6⋅3.25127…2+4⋅3.25127…+1=302656481865.62994u6=3.08501…
Δu6=∣3.08501…−3.25127…∣=0.16625…Δu6=0.16625…
u7=2.92697…:Δu7=0.15804…
f(u6)=2⋅3.08501…20+2⋅3.08501…19+2⋅3.08501…18+2⋅3.08501…17+2⋅3.08501…16+2⋅3.08501…15+2⋅3.08501…14+2⋅3.08501…13+2⋅3.08501…12+2⋅3.08501…11+2⋅3.08501…10+2⋅3.08501…9+2⋅3.08501…8+2⋅3.08501…7+2⋅3.08501…6+2⋅3.08501…5+2⋅3.08501…4+2⋅3.08501…3+2⋅3.08501…2+3.08501…+1=18043992829.22628f′(u6)=40⋅3.08501…19+38⋅3.08501…18+36⋅3.08501…17+34⋅3.08501…16+32⋅3.08501…15+30⋅3.08501…14+28⋅3.08501…13+26⋅3.08501…12+24⋅3.08501…11+22⋅3.08501…10+20⋅3.08501…9+18⋅3.08501…8+16⋅3.08501…7+14⋅3.08501…6+12⋅3.08501…5+10⋅3.08501…4+8⋅3.08501…3+6⋅3.08501…2+4⋅3.08501…+1=114172983680.20372u7=2.92697…
Δu7=∣2.92697…−3.08501…∣=0.15804…Δu7=0.15804…
u8=2.77673…:Δu8=0.15024…
f(u7)=2⋅2.92697…20+2⋅2.92697…19+2⋅2.92697…18+2⋅2.92697…17+2⋅2.92697…16+2⋅2.92697…15+2⋅2.92697…14+2⋅2.92697…13+2⋅2.92697…12+2⋅2.92697…11+2⋅2.92697…10+2⋅2.92697…9+2⋅2.92697…8+2⋅2.92697…7+2⋅2.92697…6+2⋅2.92697…5+2⋅2.92697…4+2⋅2.92697…3+2⋅2.92697…2+2.92697…+1=6470833347.00402f′(u7)=40⋅2.92697…19+38⋅2.92697…18+36⋅2.92697…17+34⋅2.92697…16+32⋅2.92697…15+30⋅2.92697…14+28⋅2.92697…13+26⋅2.92697…12+24⋅2.92697…11+22⋅2.92697…10+20⋅2.92697…9+18⋅2.92697…8+16⋅2.92697…7+14⋅2.92697…6+12⋅2.92697…5+10⋅2.92697…4+8⋅2.92697…3+6⋅2.92697…2+4⋅2.92697…+1=43067856733.97665u8=2.77673…
Δu8=∣2.77673…−2.92697…∣=0.15024…Δu8=0.15024…
u9=2.63387…:Δu9=0.14285…
f(u8)=2⋅2.77673…20+2⋅2.77673…19+2⋅2.77673…18+2⋅2.77673…17+2⋅2.77673…16+2⋅2.77673…15+2⋅2.77673…14+2⋅2.77673…13+2⋅2.77673…12+2⋅2.77673…11+2⋅2.77673…10+2⋅2.77673…9+2⋅2.77673…8+2⋅2.77673…7+2⋅2.77673…6+2⋅2.77673…5+2⋅2.77673…4+2⋅2.77673…3+2⋅2.77673…2+2.77673…+1=2320680563.35344…f′(u8)=40⋅2.77673…19+38⋅2.77673…18+36⋅2.77673…17+34⋅2.77673…16+32⋅2.77673…15+30⋅2.77673…14+28⋅2.77673…13+26⋅2.77673…12+24⋅2.77673…11+22⋅2.77673…10+20⋅2.77673…9+18⋅2.77673…8+16⋅2.77673…7+14⋅2.77673…6+12⋅2.77673…5+10⋅2.77673…4+8⋅2.77673…3+6⋅2.77673…2+4⋅2.77673…+1=16244812495.12528u9=2.63387…
Δu9=∣2.63387…−2.77673…∣=0.14285…Δu9=0.14285…
u10=2.49802…:Δu10=0.13585…
f(u9)=2⋅2.63387…20+2⋅2.63387…19+2⋅2.63387…18+2⋅2.63387…17+2⋅2.63387…16+2⋅2.63387…15+2⋅2.63387…14+2⋅2.63387…13+2⋅2.63387…12+2⋅2.63387…11+2⋅2.63387…10+2⋅2.63387…9+2⋅2.63387…8+2⋅2.63387…7+2⋅2.63387…6+2⋅2.63387…5+2⋅2.63387…4+2⋅2.63387…3+2⋅2.63387…2+2.63387…+1=832346488.77442…f′(u9)=40⋅2.63387…19+38⋅2.63387…18+36⋅2.63387…17+34⋅2.63387…16+32⋅2.63387…15+30⋅2.63387…14+28⋅2.63387…13+26⋅2.63387…12+24⋅2.63387…11+22⋅2.63387…10+20⋅2.63387…9+18⋅2.63387…8+16⋅2.63387…7+14⋅2.63387…6+12⋅2.63387…5+10⋅2.63387…4+8⋅2.63387…3+6⋅2.63387…2+4⋅2.63387…+1=6126907579.45191…u10=2.49802…
Δu10=∣2.49802…−2.63387…∣=0.13585…Δu10=0.13585…
u11=2.36880…:Δu11=0.12921…
f(u10)=2⋅2.49802…20+2⋅2.49802…19+2⋅2.49802…18+2⋅2.49802…17+2⋅2.49802…16+2⋅2.49802…15+2⋅2.49802…14+2⋅2.49802…13+2⋅2.49802…12+2⋅2.49802…11+2⋅2.49802…10+2⋅2.49802…9+2⋅2.49802…8+2⋅2.49802…7+2⋅2.49802…6+2⋅2.49802…5+2⋅2.49802…4+2⋅2.49802…3+2⋅2.49802…2+2.49802…+1=298561855.74542…f′(u10)=40⋅2.49802…19+38⋅2.49802…18+36⋅2.49802…17+34⋅2.49802…16+32⋅2.49802…15+30⋅2.49802…14+28⋅2.49802…13+26⋅2.49802…12+24⋅2.49802…11+22⋅2.49802…10+20⋅2.49802…9+18⋅2.49802…8+16⋅2.49802…7+14⋅2.49802…6+12⋅2.49802…5+10⋅2.49802…4+8⋅2.49802…3+6⋅2.49802…2+4⋅2.49802…+1=2310601127.77513…u11=2.36880…
Δu11=∣2.36880…−2.49802…∣=0.12921…Δu11=0.12921…
u12=2.24587…:Δu12=0.12293…
f(u11)=2⋅2.36880…20+2⋅2.36880…19+2⋅2.36880…18+2⋅2.36880…17+2⋅2.36880…16+2⋅2.36880…15+2⋅2.36880…14+2⋅2.36880…13+2⋅2.36880…12+2⋅2.36880…11+2⋅2.36880…10+2⋅2.36880…9+2⋅2.36880…8+2⋅2.36880…7+2⋅2.36880…6+2⋅2.36880…5+2⋅2.36880…4+2⋅2.36880…3+2⋅2.36880…2+2.36880…+1=107106520.29046…f′(u11)=40⋅2.36880…19+38⋅2.36880…18+36⋅2.36880…17+34⋅2.36880…16+32⋅2.36880…15+30⋅2.36880…14+28⋅2.36880…13+26⋅2.36880…12+24⋅2.36880…11+22⋅2.36880…10+20⋅2.36880…9+18⋅2.36880…8+16⋅2.36880…7+14⋅2.36880…6+12⋅2.36880…5+10⋅2.36880…4+8⋅2.36880…3+6⋅2.36880…2+4⋅2.36880…+1=871274563.57524…u12=2.24587…
Δu12=∣2.24587…−2.36880…∣=0.12293…Δu12=0.12293…
u13=2.12888…:Δu13=0.11698…
f(u12)=2⋅2.24587…20+2⋅2.24587…19+2⋅2.24587…18+2⋅2.24587…17+2⋅2.24587…16+2⋅2.24587…15+2⋅2.24587…14+2⋅2.24587…13+2⋅2.24587…12+2⋅2.24587…11+2⋅2.24587…10+2⋅2.24587…9+2⋅2.24587…8+2⋅2.24587…7+2⋅2.24587…6+2⋅2.24587…5+2⋅2.24587…4+2⋅2.24587…3+2⋅2.24587…2+2.24587…+1=38429268.19821…f′(u12)=40⋅2.24587…19+38⋅2.24587…18+36⋅2.24587…17+34⋅2.24587…16+32⋅2.24587…15+30⋅2.24587…14+28⋅2.24587…13+26⋅2.24587…12+24⋅2.24587…11+22⋅2.24587…10+20⋅2.24587…9+18⋅2.24587…8+16⋅2.24587…7+14⋅2.24587…6+12⋅2.24587…5+10⋅2.24587…4+8⋅2.24587…3+6⋅2.24587…2+4⋅2.24587…+1=328486438.92554…u13=2.12888…
Δu13=∣2.12888…−2.24587…∣=0.11698…Δu13=0.11698…
u14=2.01751…:Δu14=0.11137…
f(u13)=2⋅2.12888…20+2⋅2.12888…19+2⋅2.12888…18+2⋅2.12888…17+2⋅2.12888…16+2⋅2.12888…15+2⋅2.12888…14+2⋅2.12888…13+2⋅2.12888…12+2⋅2.12888…11+2⋅2.12888…10+2⋅2.12888…9+2⋅2.12888…8+2⋅2.12888…7+2⋅2.12888…6+2⋅2.12888…5+2⋅2.12888…4+2⋅2.12888…3+2⋅2.12888…2+2.12888…+1=13790835.58464…f′(u13)=40⋅2.12888…19+38⋅2.12888…18+36⋅2.12888…17+34⋅2.12888…16+32⋅2.12888…15+30⋅2.12888…14+28⋅2.12888…13+26⋅2.12888…12+24⋅2.12888…11+22⋅2.12888…10+20⋅2.12888…9+18⋅2.12888…8+16⋅2.12888…7+14⋅2.12888…6+12⋅2.12888…5+10⋅2.12888…4+8⋅2.12888…3+6⋅2.12888…2+4⋅2.12888…+1=123820714.41332…u14=2.01751…
Δu14=∣2.01751…−2.12888…∣=0.11137…Δu14=0.11137…
u15=1.91142…:Δu15=0.10608…
f(u14)=2⋅2.01751…20+2⋅2.01751…19+2⋅2.01751…18+2⋅2.01751…17+2⋅2.01751…16+2⋅2.01751…15+2⋅2.01751…14+2⋅2.01751…13+2⋅2.01751…12+2⋅2.01751…11+2⋅2.01751…10+2⋅2.01751…9+2⋅2.01751…8+2⋅2.01751…7+2⋅2.01751…6+2⋅2.01751…5+2⋅2.01751…4+2⋅2.01751…3+2⋅2.01751…2+2.01751…+1=4950229.82773…f′(u14)=40⋅2.01751…19+38⋅2.01751…18+36⋅2.01751…17+34⋅2.01751…16+32⋅2.01751…15+30⋅2.01751…14+28⋅2.01751…13+26⋅2.01751…12+24⋅2.01751…11+22⋅2.01751…10+20⋅2.01751…9+18⋅2.01751…8+16⋅2.01751…7+14⋅2.01751…6+12⋅2.01751…5+10⋅2.01751…4+8⋅2.01751…3+6⋅2.01751…2+4⋅2.01751…+1=46661280.69367…u15=1.91142…
Δu15=∣1.91142…−2.01751…∣=0.10608…Δu15=0.10608…
u16=1.81030…:Δu16=0.10111…
f(u15)=2⋅1.91142…20+2⋅1.91142…19+2⋅1.91142…18+2⋅1.91142…17+2⋅1.91142…16+2⋅1.91142…15+2⋅1.91142…14+2⋅1.91142…13+2⋅1.91142…12+2⋅1.91142…11+2⋅1.91142…10+2⋅1.91142…9+2⋅1.91142…8+2⋅1.91142…7+2⋅1.91142…6+2⋅1.91142…5+2⋅1.91142…4+2⋅1.91142…3+2⋅1.91142…2+1.91142…+1=1777460.56654…f′(u15)=40⋅1.91142…19+38⋅1.91142…18+36⋅1.91142…17+34⋅1.91142…16+32⋅1.91142…15+30⋅1.91142…14+28⋅1.91142…13+26⋅1.91142…12+24⋅1.91142…11+22⋅1.91142…10+20⋅1.91142…9+18⋅1.91142…8+16⋅1.91142…7+14⋅1.91142…6+12⋅1.91142…5+10⋅1.91142…4+8⋅1.91142…3+6⋅1.91142…2+4⋅1.91142…+1=17578062.54966…u16=1.81030…
Δu16=∣1.81030…−1.91142…∣=0.10111…Δu16=0.10111…
u17=1.71383…:Δu17=0.09646…
f(u16)=2⋅1.81030…20+2⋅1.81030…19+2⋅1.81030…18+2⋅1.81030…17+2⋅1.81030…16+2⋅1.81030…15+2⋅1.81030…14+2⋅1.81030…13+2⋅1.81030…12+2⋅1.81030…11+2⋅1.81030…10+2⋅1.81030…9+2⋅1.81030…8+2⋅1.81030…7+2⋅1.81030…6+2⋅1.81030…5+2⋅1.81030…4+2⋅1.81030…3+2⋅1.81030…2+1.81030…+1=638502.05884…f′(u16)=40⋅1.81030…19+38⋅1.81030…18+36⋅1.81030…17+34⋅1.81030…16+32⋅1.81030…15+30⋅1.81030…14+28⋅1.81030…13+26⋅1.81030…12+24⋅1.81030…11+22⋅1.81030…10+20⋅1.81030…9+18⋅1.81030…8+16⋅1.81030…7+14⋅1.81030…6+12⋅1.81030…5+10⋅1.81030…4+8⋅1.81030…3+6⋅1.81030…2+4⋅1.81030…+1=6618867.78758…u17=1.71383…
Δu17=∣1.71383…−1.81030…∣=0.09646…Δu17=0.09646…
u18=1.62169…:Δu18=0.09214…
f(u17)=2⋅1.71383…20+2⋅1.71383…19+2⋅1.71383…18+2⋅1.71383…17+2⋅1.71383…16+2⋅1.71383…15+2⋅1.71383…14+2⋅1.71383…13+2⋅1.71383…12+2⋅1.71383…11+2⋅1.71383…10+2⋅1.71383…9+2⋅1.71383…8+2⋅1.71383…7+2⋅1.71383…6+2⋅1.71383…5+2⋅1.71383…4+2⋅1.71383…3+2⋅1.71383…2+1.71383…+1=229500.02828…f′(u17)=40⋅1.71383…19+38⋅1.71383…18+36⋅1.71383…17+34⋅1.71383…16+32⋅1.71383…15+30⋅1.71383…14+28⋅1.71383…13+26⋅1.71383…12+24⋅1.71383…11+22⋅1.71383…10+20⋅1.71383…9+18⋅1.71383…8+16⋅1.71383…7+14⋅1.71383…6+12⋅1.71383…5+10⋅1.71383…4+8⋅1.71383…3+6⋅1.71383…2+4⋅1.71383…+1=2490671.57675…u18=1.62169…
Δu18=∣1.62169…−1.71383…∣=0.09214…Δu18=0.09214…
u19=1.53352…:Δu19=0.08816…
f(u18)=2⋅1.62169…20+2⋅1.62169…19+2⋅1.62169…18+2⋅1.62169…17+2⋅1.62169…16+2⋅1.62169…15+2⋅1.62169…14+2⋅1.62169…13+2⋅1.62169…12+2⋅1.62169…11+2⋅1.62169…10+2⋅1.62169…9+2⋅1.62169…8+2⋅1.62169…7+2⋅1.62169…6+2⋅1.62169…5+2⋅1.62169…4+2⋅1.62169…3+2⋅1.62169…2+1.62169…+1=82559.70843…f′(u18)=40⋅1.62169…19+38⋅1.62169…18+36⋅1.62169…17+34⋅1.62169…16+32⋅1.62169…15+30⋅1.62169…14+28⋅1.62169…13+26⋅1.62169…12+24⋅1.62169…11+22⋅1.62169…10+20⋅1.62169…9+18⋅1.62169…8+16⋅1.62169…7+14⋅1.62169…6+12⋅1.62169…5+10⋅1.62169…4+8⋅1.62169…3+6⋅1.62169…2+4⋅1.62169…+1=936373.05744…u19=1.53352…
Δu19=∣1.53352…−1.62169…∣=0.08816…Δu19=0.08816…
u20=1.44893…:Δu20=0.08458…
f(u19)=2⋅1.53352…20+2⋅1.53352…19+2⋅1.53352…18+2⋅1.53352…17+2⋅1.53352…16+2⋅1.53352…15+2⋅1.53352…14+2⋅1.53352…13+2⋅1.53352…12+2⋅1.53352…11+2⋅1.53352…10+2⋅1.53352…9+2⋅1.53352…8+2⋅1.53352…7+2⋅1.53352…6+2⋅1.53352…5+2⋅1.53352…4+2⋅1.53352…3+2⋅1.53352…2+1.53352…+1=29736.26727…f′(u19)=40⋅1.53352…19+38⋅1.53352…18+36⋅1.53352…17+34⋅1.53352…16+32⋅1.53352…15+30⋅1.53352…14+28⋅1.53352…13+26⋅1.53352…12+24⋅1.53352…11+22⋅1.53352…10+20⋅1.53352…9+18⋅1.53352…8+16⋅1.53352…7+14⋅1.53352…6+12⋅1.53352…5+10⋅1.53352…4+8⋅1.53352…3+6⋅1.53352…2+4⋅1.53352…+1=351551.64069…u20=1.44893…
Δu20=∣1.44893…−1.53352…∣=0.08458…Δu20=0.08458…
u21=1.36746…:Δu21=0.08146…
f(u20)=2⋅1.44893…20+2⋅1.44893…19+2⋅1.44893…18+2⋅1.44893…17+2⋅1.44893…16+2⋅1.44893…15+2⋅1.44893…14+2⋅1.44893…13+2⋅1.44893…12+2⋅1.44893…11+2⋅1.44893…10+2⋅1.44893…9+2⋅1.44893…8+2⋅1.44893…7+2⋅1.44893…6+2⋅1.44893…5+2⋅1.44893…4+2⋅1.44893…3+2⋅1.44893…2+1.44893…+1=10730.28828…f′(u20)=40⋅1.44893…19+38⋅1.44893…18+36⋅1.44893…17+34⋅1.44893…16+32⋅1.44893…15+30⋅1.44893…14+28⋅1.44893…13+26⋅1.44893…12+24⋅1.44893…11+22⋅1.44893…10+20⋅1.44893…9+18⋅1.44893…8+16⋅1.44893…7+14⋅1.44893…6+12⋅1.44893…5+10⋅1.44893…4+8⋅1.44893…3+6⋅1.44893…2+4⋅1.44893…+1=131710.17919…u21=1.36746…
Δu21=∣1.36746…−1.44893…∣=0.08146…Δu21=0.08146…
u22=1.28850…:Δu22=0.07896…
f(u21)=2⋅1.36746…20+2⋅1.36746…19+2⋅1.36746…18+2⋅1.36746…17+2⋅1.36746…16+2⋅1.36746…15+2⋅1.36746…14+2⋅1.36746…13+2⋅1.36746…12+2⋅1.36746…11+2⋅1.36746…10+2⋅1.36746…9+2⋅1.36746…8+2⋅1.36746…7+2⋅1.36746…6+2⋅1.36746…5+2⋅1.36746…4+2⋅1.36746…3+2⋅1.36746…2+1.36746…+1=3883.34198…f′(u21)=40⋅1.36746…19+38⋅1.36746…18+36⋅1.36746…17+34⋅1.36746…16+32⋅1.36746…15+30⋅1.36746…14+28⋅1.36746…13+26⋅1.36746…12+24⋅1.36746…11+22⋅1.36746…10+20⋅1.36746…9+18⋅1.36746…8+16⋅1.36746…7+14⋅1.36746…6+12⋅1.36746…5+10⋅1.36746…4+8⋅1.36746…3+6⋅1.36746…2+4⋅1.36746…+1=49180.53699…u22=1.28850…
Δu22=∣1.28850…−1.36746…∣=0.07896…Δu22=0.07896…
u23=1.21118…:Δu23=0.07732…
f(u22)=2⋅1.28850…20+2⋅1.28850…19+2⋅1.28850…18+2⋅1.28850…17+2⋅1.28850…16+2⋅1.28850…15+2⋅1.28850…14+2⋅1.28850…13+2⋅1.28850…12+2⋅1.28850…11+2⋅1.28850…10+2⋅1.28850…9+2⋅1.28850…8+2⋅1.28850…7+2⋅1.28850…6+2⋅1.28850…5+2⋅1.28850…4+2⋅1.28850…3+2⋅1.28850…2+1.28850…+1=1412.13758…f′(u22)=40⋅1.28850…19+38⋅1.28850…18+36⋅1.28850…17+34⋅1.28850…16+32⋅1.28850…15+30⋅1.28850…14+28⋅1.28850…13+26⋅1.28850…12+24⋅1.28850…11+22⋅1.28850…10+20⋅1.28850…9+18⋅1.28850…8+16⋅1.28850…7+14⋅1.28850…6+12⋅1.28850…5+10⋅1.28850…4+8⋅1.28850…3+6⋅1.28850…2+4⋅1.28850…+1=18261.62900…u23=1.21118…
Δu23=∣1.21118…−1.28850…∣=0.07732…Δu23=0.07732…
u24=1.13409…:Δu24=0.07708…
f(u23)=2⋅1.21118…20+2⋅1.21118…19+2⋅1.21118…18+2⋅1.21118…17+2⋅1.21118…16+2⋅1.21118…15+2⋅1.21118…14+2⋅1.21118…13+2⋅1.21118…12+2⋅1.21118…11+2⋅1.21118…10+2⋅1.21118…9+2⋅1.21118…8+2⋅1.21118…7+2⋅1.21118…6+2⋅1.21118…5+2⋅1.21118…4+2⋅1.21118…3+2⋅1.21118…2+1.21118…+1=517.69016…f′(u23)=40⋅1.21118…19+38⋅1.21118…18+36⋅1.21118…17+34⋅1.21118…16+32⋅1.21118…15+30⋅1.21118…14+28⋅1.21118…13+26⋅1.21118…12+24⋅1.21118…11+22⋅1.21118…10+20⋅1.21118…9+18⋅1.21118…8+16⋅1.21118…7+14⋅1.21118…6+12⋅1.21118…5+10⋅1.21118…4+8⋅1.21118…3+6⋅1.21118…2+4⋅1.21118…+1=6715.60947…u24=1.13409…
Δu24=∣1.13409…−1.21118…∣=0.07708…Δu24=0.07708…
u25=1.05480…:Δu25=0.07929…
f(u24)=2⋅1.13409…20+2⋅1.13409…19+2⋅1.13409…18+2⋅1.13409…17+2⋅1.13409…16+2⋅1.13409…15+2⋅1.13409…14+2⋅1.13409…13+2⋅1.13409…12+2⋅1.13409…11+2⋅1.13409…10+2⋅1.13409…9+2⋅1.13409…8+2⋅1.13409…7+2⋅1.13409…6+2⋅1.13409…5+2⋅1.13409…4+2⋅1.13409…3+2⋅1.13409…2+1.13409…+1=192.47985…f′(u24)=40⋅1.13409…19+38⋅1.13409…18+36⋅1.13409…17+34⋅1.13409…16+32⋅1.13409…15+30⋅1.13409…14+28⋅1.13409…13+26⋅1.13409…12+24⋅1.13409…11+22⋅1.13409…10+20⋅1.13409…9+18⋅1.13409…8+16⋅1.13409…7+14⋅1.13409…6+12⋅1.13409…5+10⋅1.13409…4+8⋅1.13409…3+6⋅1.13409…2+4⋅1.13409…+1=2427.51025…u25=1.05480…
Δu25=∣1.05480…−1.13409…∣=0.07929…Δu25=0.07929…
u26=0.96859…:Δu26=0.08620…
f(u25)=2⋅1.05480…20+2⋅1.05480…19+2⋅1.05480…18+2⋅1.05480…17+2⋅1.05480…16+2⋅1.05480…15+2⋅1.05480…14+2⋅1.05480…13+2⋅1.05480…12+2⋅1.05480…11+2⋅1.05480…10+2⋅1.05480…9+2⋅1.05480…8+2⋅1.05480…7+2⋅1.05480…6+2⋅1.05480…5+2⋅1.05480…4+2⋅1.05480…3+2⋅1.05480…2+1.05480…+1=73.34809…f′(u25)=40⋅1.05480…19+38⋅1.05480…18+36⋅1.05480…17+34⋅1.05480…16+32⋅1.05480…15+30⋅1.05480…14+28⋅1.05480…13+26⋅1.05480…12+24⋅1.05480…11+22⋅1.05480…10+20⋅1.05480…9+18⋅1.05480…8+16⋅1.05480…7+14⋅1.05480…6+12⋅1.05480…5+10⋅1.05480…4+8⋅1.05480…3+6⋅1.05480…2+4⋅1.05480…+1=850.85072…u26=0.96859…
Δu26=∣0.96859…−1.05480…∣=0.08620…Δu26=0.08620…
해결 방법을 찾을 수 없습니다
해결책은솔루션없음u∈R
해결책은u=0,u=1
뒤로 대체 u=sin(x)sin(x)=0,sin(x)=1
sin(x)=0,sin(x)=1
sin(x)=0:x=2πn,x=π+2πn
sin(x)=0
일반 솔루션 sin(x)=0
sin(x) 주기율표 2πn 주기:
x06π4π3π2π32π43π65πsin(x)02122231232221xπ67π45π34π23π35π47π611πsin(x)0−21−22−23−1−23−22−21
x=0+2πn,x=π+2πn
x=0+2πn,x=π+2πn
x=0+2πn해결 :x=2πn
x=0+2πn
0+2πn=2πnx=2πn
x=2πn,x=π+2πn
sin(x)=1:x=2π+2πn
sin(x)=1
일반 솔루션 sin(x)=1
sin(x) 주기율표 2πn 주기:
x06π4π3π2π32π43π65πsin(x)02122231232221xπ67π45π34π23π35π47π611πsin(x)0−21−22−23−1−23−22−21
x=2π+2πn
x=2π+2πn
모든 솔루션 결합x=2πn,x=π+2πn,x=2π+2πn