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Q.

Let f(x)=(tanx+sinx)2 . Then

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a

limit does not exist to f(x)

b

f(x) is not continuous at x=0

c

f(x) is not differentiable at x=0

d

f'0=0

answer is D.

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Detailed Solution

f(x)=tanx+sinx2we know that sinx and tanx are both continuous and differentiable at x=0Therefore, the fuciton is continuous and differentiablef'x=2tanx+sinxsec2x+cosxf'0=0
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Let f(x)=(tanx+sinx)2 . Then