Question

Examine the continuity of the function
f(x) =sin x- cos x, for x ≠ 0

      =- 1 ,forx=0

at the poinl x = 0

Answer 1

`f(0)=-1`

`and lim_(x->0)f(x)`

`=lim_(x->0)(sinx-cosx)=-1`

`therefore f(0)=lim_(x->0)f(x)`

Hence f (x)  is continuous at x = 0