Question

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​

Answer 1

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