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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