If and ,…

MATHEMATICS · Multi correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

f(x)=\frac{x\cdot2^x-x}{1-\cos x}

and

g(x)=2^x\sin\left(\frac{\log2}{2^x}\right)

, then: (1)

\lim_{x\to0}f(x)=\log2

(2)

\lim_{x\to\infty}g(x)=\log4

(3)

\lim_{x\to0}f(x)=\log4

(4)

\lim_{x\to\infty}g(x)=\log2