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Question

Discuss the continuity and differentiablity of the function f(x)=sinx+sin|x|, xR. Draw a rough sketch of the graph of f(x)

A
f(x) is continuous but not differentiable at x=0
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B
f(x) is continuous and differentiable xR,
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C
f(x) is not continuous and not derivable at x=0
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D
none of these
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Solution

The correct option is A f(x) is continuous but not differentiable at x=0
f(x)=sinx+sin|x|
f(0+)=limh0(2sinh)=0
f(0)=limh0(sinh+sinh)=0
Hence the function is continuous at x=0.
f(0+)=limh0sinh+sinhh=2
f(0)=limh0sinh+sinhh=0
Hence the function is not differentiable at x=0.

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