Finding the limits of indeterminate powers

egeise21

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Nov 10, 2011
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I have been working on this problem for days now and I just can't seem to figure it out. I am using natural logs and L'Hopital's rule but am continually coming up with an answer that doesn't make sense. I'd be so glad if someone could help me on this!


Find lim(x→0+)⁡〖(e^x+2x)10/x〗 using indeterminate powers.

PLEASE help me!
Thank you
 
I have been working on this problem for days now and I just can't seem to figure it out. I am using natural logs and L'Hopital's rule but am continually coming up with an answer that doesn't make sense. I'd be so glad if someone could help me on this!


Find lim(x→0+)⁡〖(e^x+2x)10/x〗 using indeterminate powers.

PLEASE help me!
Thank you

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
I'm stuck after doing L'Hopital's rule... my answer simplifies down to

lim(x→0+)⁡(20(ex+2))/(x2(ex+2x))

When I test to see if I can do L'Hopital's rule again, I get 20/0 as an answer, and I am not sure what to do from there.
 
If you're going to apply L'Hopital, try rewriting the limit a little.

\(\displaystyle \displaystyle e^{10\displaystyle \lim_{x\to 0}\frac{ln(e^{x}+2x)}{x}}\)

Now, apply ol' L'H:

\(\displaystyle \displaystyle e^{\displaystyle 10\lim_{x\to 0}\frac{e^{x}+2}{e^{x}+2x}}\)

Now, near 0, e approaches 1 and the 2x in the denominator approaches 0.

Can you see the limit now?.
 
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