How do you find \lim _ { x \rightarrow 1} \frac { e ^ { 2x } + e ^ { x } } { e ^ { x } - 1}?

1 Answer
Jan 14, 2018

lim_(x->1)(e^(2x)+e^x)/(e^x-1)=(e^2+e)/(e-1)~~5.88224

Explanation:

Use direct substitution. Plug in 1 for every x value:

lim_(x->1)(e^(2x)+e^x)/(e^x-1)=(e^(2(1))+e^(1))/(e^(1)-1)=(e^2+e)/(e-1)~~5.88224