How can I solve this?

lim t -> 0

(5t sec4t / tan10t)

I don't know what to do when the term is secant?

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- Jun 15th 2008, 03:55 PMtheowneTrigonometric limit...
How can I solve this?

lim t -> 0

(5t sec4t / tan10t)

I don't know what to do when the term is secant? - Jun 15th 2008, 04:20 PMMathstud28
- Jun 15th 2008, 04:24 PMtheowne
I don't understand the second line?

- Jun 15th 2008, 04:30 PMMathstud28
- Jun 15th 2008, 05:49 PMKrizalid
Mathstud28, you may consider what level is theowne currently stuying, he may won't be able to digest your post, so I suggest you to first give a stantard solution and after that, give another one with other somewhat advanced stuff.

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Now, consider which is a little fact that you should know; besides does exist, and its value is 1, hence, the original limit is - Jun 15th 2008, 06:58 PMMathstud28

Now there are a coulple of ways of going from here

Let

Now extracting a five and seeing that

and knowing that subtracting zero is legal we have

Now if you notice this looks like the definition of the derivative at a point

so

So knowing that L is our orginal limit and

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another possibility is L'hopitals

so we have

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Another possibility is this

Now we do this

Let

Now letting

we see that as

So we would have

I am sure you know the right hand limit is one

So we have

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Whew...there are a couple more but my fingers hurt (Giggle)

I did these because Krizalid is right and I felt bad so I decided to show you a couple of ways that will be at your level. Hope this helps, sorry about the earlier confusion - Jun 15th 2008, 07:04 PMtheowne
I don't really understand what you did in the final post (apart from the l'hopitals rule, which we're not allowed to use). But thanks for the help.

- Jun 15th 2008, 07:09 PMMathstud28