Question

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

• A. $\frac{11}{24}e$
• B. $\frac{11e}{24}$
• C. $\frac{e}{24}$
• D. $\frac{e}{11}$

Answer 1

The correct option is A

$\frac{11}{24}e$

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

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

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