- #1

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## Homework Statement

lim (x-> infinity) sinh(x)sinh(e^(-x))

## Homework Equations

None really.

## The Attempt at a Solution

L'Hospital?

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- Thread starter wimma
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- #1

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lim (x-> infinity) sinh(x)sinh(e^(-x))

None really.

L'Hospital?

- #2

Dick

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l'Hopital, yes. Try writing it as sinh(e^(-x))/(1/sinh(x)). Now the form is 0/0.

- #3

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hmm.. still failing at this question. pls help further?

I don't get a nice solution on applying lhospital

- #4

Dick

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What did you get from l'Hopital?

- #5

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i now get the limit to infinity of:

e^(-x)cosh(e^(-x))/(cothxcosechx)

considering substitution of y=f(x) then computing the limit for lny

- #6

Dick

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That looks ok. Now look at the parts. What's lim coth(x)? What's lim cosh(e^(-x))?

- #7

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cothx -> 1

cosechx -> 0

cosh(e^-x) -> 1

e^-x -> 0

i guess lhopital again...

- #8

Dick

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Not so fast. Aside from the stuff that goes to 1, you've got e^(-x)*sinh(x). What's that? Use the definition of sinh.

- #9

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sweet. so it's 1/2.

- #10

Dick

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Not so bad, huh?

- #11

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Nope. Must be getting tired... it's like midnight here.

- #12

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Also could u please verify that limit (x,y) -> (0,0) of (x^4*y^2)/(x^2 + y^2)2 is 0

- #13

Dick

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Express the function in polar coordinates. Count powers of r.

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