Question

Calculate the limit of the function f (x) as x approaches + ∞f (x) = (e ^ x) ¾

Answer 1

`\lim _(x\to\infty)(e^{x^{}})^{(3)/(4)}`

first we apply the property of the limit that states

`\lim _(n\to a)f(x)^b=(\lim _(n\to a)f(x))^b`

this means that we can calculate the limit apart

`\lim _(x\to\infty)e^x=\infty`

then, using the properties for infinities

`\begin{gathered} \infty^a=\infty \\ \text{then}, \\ \infty^{(3)/(4)}=\infty \\ \text{finally,} \\ \lim _(x\to\infty)(e^{x^{}})^{(3)/(4)}=\infty \end{gathered}`