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  • If <img alt="\mathrm{f(x)=\left\{\begin{array}{ll}\sin \left(\cos ^{-1} x\right)+\cos \left(\sin ^{-1} x\right), & x \leq 0 \\ \sin \left(\cos ^{-1} x\right)-\cos \left(\sin ^{-1} x\right), &am

If \mathrm{f(x)=\left\{\begin{array}{ll}\sin \left(\cos ^{-1} x\right)+\cos \left(\sin ^{-1} x\right), & x \leq 0 \\ \sin \left(\cos ^{-1} x\right)-\cos \left(\sin ^{-1} x\right), & x>0\end{array}\right.}  then at \mathrm{x= 0}

Option: 1

f(x) is continuous and differentiable


Option: 2

f(x) is continuous but not differentiable


Option: 3

f(x) not continuous but differentiable


Option: 4

f(x)  is neither continuous nor differentiable


Answers (1)

best_answer

\mathrm{f(x)= \begin{cases}2 \sqrt{1-x^{2}}, & x \leq 0 \\ 0, & x>0\end{cases}}

Clearly, \mathrm{f(x)} is discontinuous, hence non-differentiable at \mathrm{x= 0}.

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shivangi.shekhar

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