Need help with these Hospital limits:

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- Dec 17th 2006, 07:48 AMtotalnewbieLimits with L'Hopital
Need help with these Hospital limits:

- Dec 17th 2006, 08:11 AMCaptainBlack
Find: .

Rewrite as:

,

now use L'hopital's rule:

,

...............=

...............=

RonL

- Dec 17th 2006, 08:15 AMCaptainBlack
Find

The first term in the limit clearly goes to , while the second

term is a well known limit equal to , so the limit as a whole is .

Opps didn't see the actual question:

Find

but the second term still has a finite limit and so the whle thing still goes to

(or is a different interpretation of the second term in the limit meant?)

RonL - Dec 17th 2006, 08:19 AMSoroban
Hello, totalnewbie!

Here's the first one . . .

Quote:

The function goes to:

Rewrite as: . . . . which goes to

Apply L'Hopital: .

. .

- Dec 17th 2006, 09:05 AMtotalnewbie
I used Hospital rule for the second one too and got that final result is cosx*sinx. 0*1=0

Just want to see someone's confirmation. - Dec 17th 2006, 09:31 AMCaptainBlack
Third go at the second question:

Find

which seems a plausible form for what might have been intended.

(the limit is 1/3 but I will need to do some work to produce what you would

think an acceptable explanation)

The limit is:

Take the series expasion of

So:

..............

RonL - Dec 17th 2006, 09:40 AMSoroban
Hello, totalnewbie!

I am assuming that the second problem is: .

Then we have: . . . . which goes to

Apply L'Hopital: .

Divide top and bottom by

Then: .

- Dec 17th 2006, 11:28 AMtotalnewbie
Thank you Soroban!