limit as x approaches pi of cos(x+cos(x))

解答

x \to π lim (cos (x + cos (x)))

cos (π - 1)

十进制

- 0.54030 \dots

求解步骤

x \to π lim (cos (x + cos (x)))

代入值

x = π

= cos (π + cos (π))

使用以下普通恒等式:

cos (π) = (- 1)

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= cos (π - 1)

x \to 0 lim (\frac{1 - cos ( 8 x )}{1 - cos ( 3 x )})

x \to 3 lim ((x - 3)^{x - 3})

x \to 0 lim (e^{c o s (x)})

x \to 0 lim (\frac{1}{x - x ^{2}})

t \to 0 lim ((\frac{cos ( t )}{cos ( 2 t )})^{\frac{1}{t ^{2}}})