If f x = e 2 x - 1 e 2 x + 1 : x ≠ 0 0 : x = 0 , then f x is

Question

If f x = e 2 x - 1 e 2 x + 1 : x ≠ 0 0 : x = 0 , then f x is, Continuous as well as differentiable at x = 0, Continuous but not differentiable at x = 0, Differentiable but not continuous at x = 0, None of these

MARKS App · Accepted Answer

lim h → 0 + ⁡ f 0 - h = lim h → 0 + ⁡ e - 2 h - 1 e - 2 h + 1 = 0 - 1 0 + 1 = - 1 and lim h → 0 + ⁡ f 0 + h = lim h → 0 + ⁡ e 2 h - 1 e 2 h + 1 = lim h → 0 + ⁡ 1 - e - 2 h 1 + e - 2 h = 1 - 0 1 + 0 = 1 Since, lim h → 0 + ⁡ f 0 - h ≠ lim h → 0 + ⁡ f 0 + h , therefore, f x is not continuous and not differentiable at x = 0 .

Search any question & find its solution

Looking for more such questions to practice?