Question

Find the limit to 0 of....

[(e^2x)-1]/x


Is it possible to do this w/out a calculator?

Answer 1

do you know l`hopital rule yet?

Answer 2

no...
:(

Answer 3

You can't have a zero in the denominater.
The answer is 2

Answer 4

dont just give answer, help them find answer....I dont know how to solve this wthout lhopitals rule

Answer 5

@zzr0ck3r yeah, I'm trying to find a direct way to do this, without l'Hopital's

Answer 6

idk, I'm just practicing for a test and this question was online...

Answer 7

you nee to know how to tke a derivative to do this, you will lear that soon

Answer 8

I know how to take a derivative, but how will that help me solve it?

Answer 9

take the derivative of the num and the the denom. then run the limit

Answer 10

you will have (2e^2x)/1 now run the limi

Answer 11

limit*

Answer 12

Oh, I've got one:
Well we know:
\[
e^x-1\sim x\\
x\to 0
\]
So:
\[
\lim_{x\to 0}\frac{e^{2x}-1}{x}=\lim_{u\to 0}\frac{e^{u}-1}{\frac{1}{2}u}
\]Where \(u=2x\)
Due to that:
\[
\lim_{x\to 0}\frac{u}{\frac{1}{2}u}=\frac{1}{\frac{1}{2}}=2
\]