Calculus Problem #1 by Aly Ahmed

Calculus Level 2

lim ⁡ x → π π + x cos ⁡ x x − π = ? \large \lim_{x \to \pi} \frac {\pi+x \cos x}{x-\pi} = ?


The answer is -1.

Aly Ahmed by Aly Ahmed , 34, Egypt

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1 solution

L = lim ⁡ x → π π + x cos ⁡ x x − π A 0/0 case, L’H o ˆ pital’s rule applies = lim ⁡ x → π cos ⁡ x − x sin ⁡ x 1 Differentiate up and down w.r.t. x = − 1 \begin{aligned} L & = \lim_{x \to \pi} \frac {\pi + x \cos x}{x-\pi} & \small \color{#3D99F6} \text{A 0/0 case, L'Hôpital's rule applies} \\ & = \lim_{x \to \pi} \frac {\cos x-x \sin x}1 & \small \color{#3D99F6} \text{Differentiate up and down w.r.t. }x \\ & = \boxed{-1} \end{aligned}

Reference: L'Hôpital's rule

1 Helpful 0 Interesting 1 Brilliant 0 Confused

@Aly Ahmed, you should learn up LaTex since you like to set problems. The LaTex for your problem here is as follows. Do not copy the problem as title.

Chew-Seong Cheong - 1 year, 10 months ago

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