limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x}

解答

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

\frac{1}{2}

十进制

0.5

求解步骤

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

使用洛必达法则

= x \to 3 lim (\frac{sec ^{2} ( x - 3 )}{3 e ^{x - 3} - 1})

代入值

x = 3

= \frac{sec ^{2} ( 3 - 3 )}{3 e ^{3 - 3} - 1}

化简

\frac{sec ^{2} ( 3 - 3 )}{3 e ^{3 - 3} - 1} : \frac{1}{2}

= \frac{1}{2}

d er i v a t i v e \frac{1}{x ^{2} + 4}

\frac{d}{d x} (\frac{tan ( x )}{x ^{2}})

t an g e n t f (x) = \frac{4 x}{x + 3}, (1, 1)

\frac{d}{d θ} (cos (θ) - θ sin (θ))

a re a 9 x^{2}, 8 x^{4} - 8 x^{2}