Question

\(ln(lim_{x\rightarrow\infty}\frac{f(x)}{g(x)})=\lim_{x\rightarrow\infty}ln(f(x))+\lim_{x\rightarrow\infty}ln(g(x))\)

(a) True

(b) False

The question was posed to me in an international level competition.

My question is taken from Indeterminate Forms in section Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (b) False

Easiest explanation: \(ln(lim_{x\rightarrow\infty}\frac{f(x)}{g(x)})=ln(\frac{\lim_{x\rightarrow\infty}f(x)}{\lim_{x\rightarrow\infty}g(x)})\)

\(\Rightarrow ln(\lim_{x\rightarrow\infty}\frac{f(x)}{g(x)}) = \lim_{x\rightarrow\infty}ln(f(x)) – \lim_{x\rightarrow\infty}ln(g(x))\)