Question

Evaluate:

$\underset{x\to 0}{lim}\frac{e^{7x}-1}{x}$

Answer 1

Now,

$\underset{x\to 0}{lim}\frac{e^{7x}-1}{x}$

$=7\times \underset{7x\to 0}{lim}\frac{e^{7x}-1}{7x}$

[since $\underset{x\to 0}{lim}\frac{e^x-1}{x}=1$]

$=7\times 1$

$=7$.