Discuss the continuity and differentiability of `f(x)={(x-c)cos(1/(x-c))` `,x!=c and 0 ,x=c`

Explanation

`f(x)= (x-c)cos(1/(x-c)) `

`f(x)={ (x-c)cos(1/(x-c)),xne c `and
`0, x =c }`

`text { LHL }=lim _{x -> c^{-}} f(x) `

`text{LHL}=lim _{h -> 0} f({c}-h) `

`text{LHL}=lim _{h -> 0}(c-h-c)cos(1/(c-h-c)) `

`text{LHL}=lim _{h -> 0} (-h)cos(1/(-h))=0`

Now,

...