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karush

Gold Member

MHB

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**AP calculus**practice questions on

**MeWe**so thot I would pass them thru here first

The solution is mine...

any typos or suggestions...

$\textbf{Find the Limit of}$

$\displaystyle\lim_{x\to \pi} \dfrac{\cos{x}+\sin{x}+1}{x^2-\pi^2}$

(A) $-\dfrac{1}{2\pi}$

(B) $\dfrac{1}{\pi}$

(C) $1$

(D) DNE

$\textbf{Solution}$

By observation we have $\frac{0}{0}$ so apply L'Hopital's Rule

apply LH'R then plug in $\pi$ and simplify

$$\displaystyle\lim _{x\to \:\pi }

\left(\frac{\cos \left(x\right)-\sin \left(x\right)}{2x}\right)

=\dfrac{-1-0}{2\pi}=-\dfrac{1}{2\pi} \quad (A)$$