Question

Solve: $\underset{x\to 2}{lim}\frac{e^{x^2}-\cos x}{x^2}$

Answer 1

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

$=\left(\underset{x\to 2}{lim}{e}^{x^2}-\underset{x\to 2}{lim}\cos x\right)\times \underset{x\to 2}{lim}\frac{1}{x^2}$

$=\frac{e^4-\cos 2}{4}$

$\therefore \underset{x\to 2}{lim}\frac{e^{x^2}-\cos x}{x^2}=\frac{e^4-\cos 2}{4}$.