TS EAMCET · Maths · Continuity and Differentiability
If \(f(x)=|x|+|\sin x|\) for \(x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), then its left hand derivative at \(x=0\) is
- A 0
- B -1
- C -2
- D -3
Answer & Solution
Correct Answer
(C) -2
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=|x|+|\sin x| \\ & \text { LHD }=\lim _{h \rightarrow 0} \frac{f(0-h)-f(0)}{0-h} \\ & =\lim _{h \rightarrow 0} \frac{|0-h|+|\sin (0-h)|-(0+0)}{0-h} \\ & =\lim _{h \rightarrow 0} \frac{h+\sin h}{-h}=-\lim _{h \rightarrow 0}\left(1+\frac{\sin h}{h}\right) \\…
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