Question

$\underset{x\to 0}{lim}\frac{(1+x{)}^{1/x}-e+\frac{e{x}^2}{2}}{11x^2}$

Answer 1

We have,

${lim}_{x\to 0}\frac{{(1+x)}^{\frac{1}{x}}-e+\frac{e{x}^2}{2}}{11x^2}$

We know that,

${lim}_{x\to 0}{(1+x)}^{\frac{1}{x}}=e$

So,

${lim}_{x\to 0}\frac{e-e+\frac{e{x}^2}{2}}{11x^2}$

${lim}_{x\to 0}\frac{e}{22}$

Taking limit and we get,

$=\frac{e}{22}$

Hence, this is the answer.