Q 77. - Calculus

Question

Find the limit.

$\underset{x\to 0}{\lim }{\left(1+x\right)}^{\frac{2}{x}}$

Step-by-Step Solution

Answer

Answer is $e^2$

Step 1. Given information

Limit function is $\underset{x\to 0}{\lim }{\left(1+x\right)}^{\frac{2}{x}}$

Step 2. Explanation

$\begin{array}{rcl}\underset{x\to 0}{\lim }{\left(1+x\right)}^{\frac{2}{x}}& =& \underset{x\to 0}{\lim }{\left[{\left(1+x\right)}^{\frac{1}{x}}\right]}^2\\ & =& e^2\end{array}$