Question

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

• A.
• B.
• C.
  
• D.

Answer 1

The correct option is A

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