How can I solve this?
lim t -> 0
(5t sec4t / tan10t)
I don't know what to do when the term is secant?
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
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
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