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)=+∞