# Application of L'Hopital's Rule

Task:

Graph the f(x) = e^2x - 1/x

Verify the Limit x→0 f(x) meets the criteria for applying L'Hopital's Rule

Find the Limit x→0 f(x)

Explain why L'Hopital's Rule cannot be used to find the limit of Lim x→0 e^2x/x

https://brainmass.com/math/calculus-and-analysis/application-of-l-hopital-s-rule-570901

#### Solution Preview

for f(x) = (e^2x - 1)/x, if x goes to 0, then both e^2x - 1 and x go to 0. That is, ...

#### Solution Summary

The solution explains when L'Hopital's Rule works and how it works with examples.

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