Question

If $\underset{x\to 0}{\lim }\frac{(1+x{)}^{1/x}-e+\frac{1}{2}ex}{x^2}=\frac{11e}{k}$ then find $k$

Answer 1

Answer: 24.00

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