Question

What is the lim as x-->infinity (5e∧-x + 1)^2e^x

Answer 1

`\displaystyle\lim_(x\to\infty)(5\e^(-x)+1)^2e^x=\lim_(x\to\infty)((5e^(-x)+1)^2e^(2x))/(e^x)=\lim_(x\to\infty)((5+e^x)^2)/(e^x)`

Replacing
`y=e^x`, the limit is equivalent to


`\displaystyle\lim_(y\to\infty)\frac{(5+y)^2}y`

which clearly approaches
`\infty`.