Question Number 101008 by Rio Michael last updated on 29/Jun/20

Given f(x) =  { (((1/2)xe^(1/x)  , x ≠ 0)),((0, x = 0 )) :}  find  (i) Thd domain of f  (ii) check the continuity of f at x = 0  (iii) check its differentiability and its sign  (i) sketch this curve and find lim_(x→−∞)  f(x) and lim_(x→+∞)  f(x)

Answered by maths mind last updated on 29/Jun/20

D_f =R  2)  lim_(x→0^− )  f(x)=0  3)lim_(x→0^+ )  f(x)=+∞   f not continue  (iii) diffrentiabilite ⇒continuity  ⇔(no conginuity ⇒no differentiabilitie)  lim_(x→−∞) f(x) =−∞,lim_(x→+∞) f(x)=+∞