Let g(x) = ((x -1)n/ log cosm (x -1)) ; 0

Question

Let g(x) = ((x -1)n/ log cosm (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 displaystyle limx → 1+ g(x) = p , then (A) n = 1, m = 1 (B) n = 1, m = - 1 (C) n = 2, m = 2 (D) n > 2, m = n

Tardigrade Admin · Accepted Answer

Correct answer is (c) n = 2, m = 2

Q. Let $g (x) = \frac{( x - 1 ) ^{n}}{l o g c o s ^{m} ( x - 1 )}; 0 < x < 2, m$ and $n$ are integers, m $\neq =$ 0, n > 0 , and let $p$ be the left hand derivative of $∣ x - 1∣$ at $x = 1$ . If $x \to 1^{+} lim g (x) = p$ , then

$n = 1, m = 1$

$n = 1, m = - 1$

$n = 2, m = 2$

$n > 2, m = n$

Correct answer is (c) $n = 2, m = 2$

Q. Let g(x)=logcosm(x−1)(x−1)n​;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 x→1+lim​g(x)=p , then

n=1,m=1

n=1,m=−1

n=2,m=2

n>2,m=n