There is a simple fact you overlooked . . . (I almost did!)
Your work is correct . . .
Using L'Hopital, the problem becomes: .
As approches , the fraction approaches: .
Okay, so I'm working with L'Hopitals rule and indeterminate forms.. and I ran across this problem in my homework. I get the right answer, only that it is positive instead of negative and I can't figure out why it's negative.
limit (sec(3x)cos(5x)) x-> (pi/2) from the left
since that is in infinity * 0 form... I did:
= cos(5x) / (1/sec(3x)) = 0/0
Great... I can now use L'Hopitals...
= -5sin(5x) / -3sin(3x) = 5/3
Negatives cancel right?? So now where did I go wrong? The answer should be negative according to my textbook, Wolfram Alpha, and MS Math.