Find the limit.
as theta approaches 0
cos3theta - 1 / sin7theta

Any assistance would be nice :)

Question

Find the limit.
as theta approaches 0
cos3theta - 1 / sin7theta

Any assistance would be nice :)

tkhunny · Answer

You have written $\cos(3\theta) - \dfrac{1}{\sin(7\theta)}$.

Was this your intent?  If not, please use parentheses to clarify.

anonymous · Answer

$$\frac{ \cos3\theta-1 }{ \sin7\theta }$$

anonymous · Answer

@tkhunny sorry, forgot to add th parenthese around the theta

tkhunny · Answer

Don't forget your Order of Operations.  It IS important.

Okay, what does this thing do as $\theta$ shrinks toward zero?  Do we get l'hospital?

anonymous · Answer

@tkhunny yes, it goes towards zero, and I dont exactly understand how to use l'hospital

tkhunny · Answer

The question is this...

1) Do you have l'hospital at all.  Apparently, the answer to this is "yes".
2) Does l'hospital apply?  Limit of numerator alone is 0.  Limit of denominator alone is 0.  So, yes, we have a 0/0 Indeterminate Form and we can use l'hospital.

Where does that leave us?  Derivatives of numerator and denominator separately?

anonymous · Answer

$$-3\sin(3x)/7\cos(7x)$$

anonymous · Answer

@tkhunny so does that look right?

tkhunny · Answer

Yes.  Now what happens as $\theta$ shrinks?