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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Limits

NDA 2017 · Mathematics · Limits

If _ x arrow (π)/(2) ( x)/(x)=l and _ x arrow ∞ ( x)/(x)=m , then...

If lim⁡x→π2sin⁡xx=l\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=l and lim⁡x→∞cos⁡xx=m\lim _{x \rightarrow \infty} \frac{\cos x}{x}=m, then which one of the following is correct?

Options

  1. Al=1,m=1l=1, \mathrm{ m}=1
  2. Bl=2π,m=∞l=\frac{2}{\pi}, \mathrm{ m}=\infty
  3. Cl=2π,m=0l=\frac{2}{\pi}, \mathrm{ m}=0
  4. Dl=1,m=∞l=1, \mathrm{ m}=\infty

Correct answer

C. l=2π,m=0l=\frac{2}{\pi}, \mathrm{ m}=0

Step-by-step solution

lim⁡x→π2sin⁡xx=l and  lim⁡x→∞cos⁡xx=mlim⁡x→π2sin⁡xx=1π2=2π;lim⁡x→∞cos⁡xx=0\begin{aligned} & \lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=l \text{\text{ 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\end{aligned}\therefore l=\frac{2}{\pi}, \mathrm{ m}=0$
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