Question

Show that the function `f(x)={x^2sin(1/x),ifx!=0 0,ifx=0` is differentiable at `x=0` and `f^(prime)(0)=0`

Answer 1

LHD=`lim_(h->0) ((-h)^2sin(-1/h) - 0)/(-h)`
`lim_(h->0) (-h^2 sin(1/h))/(-h)`
`= lim_(h->0) h xx sin(1/h)`
`= 0`
RHD=`lim_(h->0) (h^2sin(1/h) - 0)/h `
`= lim_(h->0) h xx sin(1/h)`
`=0`
RHD`=`LHD
`:.` f(x) is diff at x= 0
Answer