Question

Discuss the differentiability of `f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a tx=0`

Answer 1

LHD=`lim_(x->0^-) (xe - (-1/x + 1/x) - 0)/(x-0) `
`= lim_(x->0^-) (xe)/x = e`
RHD= `lim_(x->0^+) (xe- (1/x + 1/x) - 0)/(x-0)`
`= lim_(x->0^+) (xe- 2/x)/x`
`= lim_(x->0^+) (x^2e-2)/(x^2) = (0-2)/0 = -oo`
LHD=`e`
RHD=`-oo`
LHD`!=`RHD
`:.` f(x) is not differentiable
Answer