Exponential function

[Kflower1]

So if I have lim--> infinity and the function ((5e^3x)+(e^x))/((7e^3x)-(e^-2x)) how do I go about evaluating the limit? I don't even know how to start this problem. Please help. Thanks for your time.

 

[Deleted member 4993]

So if I have lim--> infinity and the function ((5e^3x)+(e^x))/((7e^3x)-(e^-2x)) how do I go about evaluating the limit? I don't even know how to start this problem. Please help. Thanks for your time.

To have a better idea about the "goal", substitute:

u = e[sup:1h1h776g]x[/sup:1h1h776g]

 

[soroban]

Hello, Kflower1!

$\displaystyle \displaystyle \lim_{x\to\infty}\,\frac{5e^{3x}+e^x}{7e^{3x}- e^{\text{-}2x}}$

$\displaystyle \text{We have: }\lim_{x\to\infty} \,\frac{5e^{3x} + e^x}{7e^{3x} - \frac{1}{e^{2x}}}$

$\displaystyle \text{Divide numerator and denominator by }e^{3x}\!:$

. . $\displaystyle \lim_{x\to\infty}\,\dfrac{5 + \dfrac{1}{e^{2x}}} {7 - \dfrac{1}{e^{5x}}} \;\;=\;\;\frac{5+0}{7-0} \;\;=\;\;\frac{5}{7}$