Question

$\underset{x\to 0}{lim}\frac{e^x-\cos x}{x^2}$ is equal to

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. $\frac{2}{3}$
• D. None of the above

Answer 1

The correct option is D None of the above

Substituting gives us indeterminate form.
So, applying L'Hospitals Rule,
${lim}_{x\to 0}\frac{e^x-\cos x}{x^2}$
Sustituting gives us indeterminate form so applying L'Hospital's Rule again,
$={lim}_{x\to 0}\frac{e^x+\sin x}{2}$
$=\frac{1+1}{2}$
$=1$
Hence, option 'D' is correct.