Question

$\underset{x\to 0}{\lim }\frac{e^{x^2}-cosx}{x^2}=$

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. 1
• D. $-\frac{3}{2}$
• E. $-\frac{1}{2}$

Answer 1

Answer: (C)

$\underset{x\to 0}{\lim }\frac{e^{x^2}-\cos x}{x^2}$
$\left(1+\frac{x^2}{1!}+\frac{x^4}{2!}+\dots \infty \right)$
$=\underset{x\to 0}{\lim }\frac{-\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}-\dots \infty \right)}{x^2}$
$=\underset{x\to 0}{\lim }\frac{x^2+\left(\frac{1}{2!}-\frac{1}{4!}\right)x^4+\dots }{x^2}$
$=\underset{x\to 0}{\lim }1+\left(\frac{1}{2}-\frac{1}{24}\right)x^2+\dots =1+0\dots =1$