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Calculus Level 2

Find the value! lim ⁡ x → π sin ⁡ ( π − x ) π ( π − x ) \displaystyle \lim_{x \rightarrow \pi} \frac{\sin(\pi-x)}{\pi(\pi-x)}

Enter the answer to three decimal places.


The answer is 0.318.

Omkar Kulkarni by Omkar Kulkarni , 22, India

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2 solutions

Let u = π − x . u = \pi - x. Then u → 0 u \rightarrow 0 as x → π , x \rightarrow \pi, and so the limit becomes

1 π × lim ⁡ u → 0 sin ⁡ ( u ) u = 1 π × 1 = 0.318 \dfrac{1}{\pi} \times \lim_{u \rightarrow 0} \dfrac{\sin(u)}{u} = \dfrac{1}{\pi} \times 1 = \boxed{0.318} to 3 decimal places.

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Shivam Sharma
Apr 26, 2015

USE L'HOSPITAL'S RULE

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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