Question

The integer n for which $\underset{x\to 0}{\text{lim}}\frac{(\cos x-1)(\cos x-e^x)}{x^n}$ is a finite non-zero number is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

$\underset{x\to 0}{\text{lim}}\frac{(\frac{-x^2}{2!}+\frac{x^4}{4!}.....)(-x-x^2+...)}{x^n}$ is non-zero if $n=3$