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a
f is continuous and differentiable at every point
b
f is continuous at every point but is not differentiable everywhere
c
f is differentiable at every point
d
f is differentiable only at the origin
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Correct option is B
f0−=limx→0−xe1x−e-1xe1x+e-1x =limx→0-xe2x-1e2x+1 =limx→0x0-10+1=0f0+=limx→0+x1−e−2x1+e-2x =limx→0+x1−01+0=0f(0)=0 (given) So, f is continuous everywhere f'(0-)=limk→0-he1h-e-1he1h+e-1h-0h =0-10+1=-1f'0+=limh→0+he1h−e-1he1h+e-1h−0h =1 ∴ f'0−≠f'0+Similar Questions
Let then all the number of points where is not differentiable is (are)
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