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

Sagot :

[tex]\lim _{x\to\infty}(e^{x^{}})^{\frac{3}{4}}[/tex]

first we apply the property of the limit that states

[tex]\lim _{n\to a}f(x)^b=(\lim _{n\to a}f(x))^b[/tex]

this means that we can calculate the limit apart

[tex]\lim _{x\to\infty}e^x=\infty[/tex]

then, using the properties for infinities

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

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