find limit as x approach 0 : [cos(2x) -1]/sin7x
Can anyone explain how I can start this problem? I am clueless!
Hi NeoSonata,
Since both the numerator and denominator tends to zero as x tends to zero, this is an indeterminate form. I suggest you use the L'Hôpital's rule.
Yes that is correct. I think you have to understand the L'Hôpital's rule. So I will briefly explain. Suppose you have to evaluate a limit of the form, where f(x) and g(x) are two differentiable functions and
Then the L'Hôpital's rule says that,
So in this case you have to evaluate,
A more detailed (and easily understandable) description about the L'Hôpital's rule could be found at, Pauls Online Notes : Calculus I - L'Hospital's Rule and Indeterminate Forms
Hello, NeoSonata!
From the "shape" of the problem, I suspect these theorems are suggested:
. .
We have: .
Multiply the first fraction by , the second by
. .
. . . . .
. . . . .
Edit: Ah, HallsofIvy beat me to it! . . . *sigh*