Q. 52 - Calculus

Question

$\underset{x\to 1}{\lim }\left(\frac{e^x-1}{e^{2x}+2e^x-3}\right)$

Step-by-Step Solution

Answer

$\underset{x\to 1}{\lim }\left(\frac{e^x-1}{e^{2x}+2e^x-3}\right)=\frac{e-1}{e^2+2e-3}$

Step 1. Given information

$\underset{x\to 1}{\lim }\left(\frac{e^x-1}{e^{2x}+2e^x-3}\right)$

Step 2. Plug in the values

$\underset{x\to 1}{\lim }\left(\frac{e^x-1}{e^{2x}+2e^x-3}\right)=\frac{e^1-1}{e^{2·\hspace{0.17em}1}+2e^1-3}$

$\underset{x\to 1}{\lim }\left(\frac{e^x-1}{e^{2x}+2e^x-3}\right)=\frac{e-1}{e^2+2e-3}$