AP EAMCET · Maths · Continuity and Differentiability
Which of the following is differentiable at \(x=0 ?\)
- A \(f(x)=\cos |x|+|x|\)
- B \(f(x)=\sin |x|+|x|\)
- C \(f(x)=\cos |x|-|x|\)
- D \(f(x)=\sin |x|-|x|\)
Answer & Solution
Correct Answer
(D) \(f(x)=\sin |x|-|x|\)
Step-by-step Solution
Detailed explanation
At \(x=0\), RHD \(\sin |x|-|x|=\lim _{h \rightarrow 0} \frac{(\sin |h|-|h|-(0)}{h}\) \(\begin{aligned} & =\lim _{h \rightarrow 0}\left(\frac{\sin h}{h}-1\right) \\ & =1-1=0\end{aligned}\) LHD of \(\sin |x|-|x|=\lim _{h \rightarrow 0} \frac{(\sin |-h|-|-h|)}{-h}=0\)…
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