Question

The value of $\underset{x\to 0}{lim}\frac{(1+x{)}^{1/x}-e+\frac{1}{2}ex}{x^2}$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\underset{x\to 0}{lim}\frac{(1+x{)}^{1/x}-e+\frac{1}{2}ex}{x^2}$

=$\underset{x\to 0}{lim}\frac{e(1-\frac{x}{2}+\frac{11}{24}{x}^2+...)-e+\frac{1}{2}ex}{x^2}$

=$\underset{x\to 0}{lim}\frac{\frac{11}{24}e{x}^2+...}{x^2}$ = $\frac{11}{24}e$