Let , , and let be the left-hand derivative of at . If ,…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let g(x)=(x−1)nlog⁡cos⁡m(x−1)g(x) = \frac{(x-1)^n}{\log \cos^m (x-1)}, 0<x<20 < x < 2, where mm and nn are integers, m≠0m \neq 0, n>0n > 0, and let pp be the left-hand derivative of ∣x−1∣|x-1| at x=1x=1. If lim⁡x→1+g(x)=p\lim_{x \to 1^+} g(x) = p, then (1) n=1,m=1n=1, m=1 (2) n=1,m=−1n=1, m=-1 (3) n=2,m=2n=2, m=2 (4) n>2,m=nn>2, m=n

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