Finding the limit of x ^ 2 * e ^ 1 / X when x tends to 0

Finding the limit of x ^ 2 * e ^ 1 / X when x tends to 0

Let t = 1 / x, X - > 0, T - > ∞ LIM (x - > 0) x & # 178; / e ^ (1 / x) = LIM (T - > ∞) e ^ (- t) / T & # 178; LIM (x - > 0 +) X & # 178; / e ^ (1 / x) = LIM (T - > + ∞) e ^ (- t) / T & # 178; = 0lim (x - > 0 -) x & # 178; / e ^ (1 / x) = LIM (T - > - ∞) e ^ (- t) / T & #