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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Limits

BITSAT 2023 · Paper 1 · Mathematics · Limits

_ x arrow 0 (| x|)/(x) is equal to

lim⁡x→0∣sin⁡x∣x\lim _{x \rightarrow 0} \frac{|\sin x|}{x} is equal to

Options

  1. A1
  2. B-1
  3. CDoes not exist
  4. DNone of these

Correct answer

C. Does not exist

Step-by-step solution

Let l=lim⁡x→0[sin⁡x]x;RHL=lim⁡x→0+sin⁡xx=1l=\lim _{x \rightarrow 0} \frac{[\sin x]}{x} ; \mathrm{RHL}=\lim _{x \rightarrow 0^{+}} \frac{\sin x}{x}=1
LHL=lim⁡x→0−(−sin⁡xx)=−(lim⁡x→0−sin⁡xx)=−1\mathrm{LHL}=\lim _{x \rightarrow 0^{-}}\left(\frac{-\sin x}{x}\right)=-\left(\lim _{x \rightarrow 0^{-}} \frac{\sin x}{x}\right)=-1
\left[|x|=x if x≥0−x if x≤0\begin{array}{c}x \text{ if } x \geq 0 \\ -x \text{ if } x \leq 0\end{array}\right]
As, LHL ≠ RHL Hence, limit ll.does not exist.
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