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If $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=$ and $\lim _{x \rightarrow \infty} \frac{\cos x}{x}=m$, then which one of the
following is correct?
Options:
following is correct?
Solution:
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Verified Answer
The correct answer is:
$l=\frac{2}{\pi}, \mathrm{m}=0$
$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=l$ and $\lim _{x \rightarrow \infty} \frac{\cos x}{x}=m$
$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=\frac{1}{\frac{\pi}{2}}=\frac{2}{\pi} ; \lim _{x \rightarrow \infty} \frac{\cos x}{x}=0$
$\therefore l=\frac{2}{\pi}, \mathrm{m}=0$
$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=\frac{1}{\frac{\pi}{2}}=\frac{2}{\pi} ; \lim _{x \rightarrow \infty} \frac{\cos x}{x}=0$
$\therefore l=\frac{2}{\pi}, \mathrm{m}=0$
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