Question

Let g(x) = (x - 1)ⁿ/(log cos^m(x - 1)); 0 < x < 2, m and n are integers, m ≠ 0, n > 0 and let p be the left hand derivative of |x - 1| at x = 1 . If lim g(x) = p, then

(a) n = 1, m = 1

(b) n = 1, m = -1

(c) n = 2, m = 2

(d) n > 2, m = n

Answer 1

Correct option (c) n = 2, m = 2

Explanation :

Given,

n are integers and

The left hand derivative of | x - 1 | at x = 1 is p = -1

(using L'Hospital's rule)

Comments

Correct :-)