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Question

The function f(x)=1+|sinx| is

A
continuous nowhere
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B
continuous' everywhere
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C
differentiable nowhere
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D
not differentiable at x = 0
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E
not differentiable at an infinite number of
points.
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Solution

The correct options are
A continuous' everywhere
C not differentiable at x = 0
E not differentiable at an infinite number of
points.
f(x)={1+sinx for sinx01sinx for sinx<0
Clearly f(x) is continuous everywhere.
f(x)={cosx for sinx0cosx for sinx<0
f is differentiable everywhere except at the points where sinx=0,
i.e., x=nπ, nϵI. Hence f is also not differentiable at x=0.

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