show that the following function is not differentiable at x=0 f(x)=x^2 e^1/x-e^-1/x/e^1/x+e^1/x , x=0 and f(x)=0 when x=0
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Answer:
Step-by-step explanation:
Given f(x) is continuous at x=0
LHL=RHL=f(0)
f(x)=
e
1/x
+e
−1/x
x(e
1/x
−e
−1/x
)
f(x)=
1+e
−2/x
x(1−e
−2/x
)
So,
x→0
lim
1+e
−2/x
x(1−e
−2/x
)
=0
⇒f(0)=0
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