How can I solve this?

lim t -> 0

(5t sec4t / tan10t)

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

Printable View

- June 15th 2008, 02:55 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? - June 15th 2008, 03:20 PMMathstud28
- June 15th 2008, 03:24 PMtheowne
I don't understand the second line?

- June 15th 2008, 03:30 PMMathstud28
- June 15th 2008, 04:49 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.

-----

Now, consider which is a little fact that you should know; besides does exist, and its value is 1, hence, the original limit is - June 15th 2008, 05:58 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

----------------------------------------------------------------------

another possibility is L'hopitals

so we have

----------------------------------------------------------------------

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

------------------------------------------------------------

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 - June 15th 2008, 06:04 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.

- June 15th 2008, 06:09 PMMathstud28