limits and derivatives of equations using trig functions

[kristoball]

hello, i'm just looking for help with a few problems involving trig function derivatives. I know the formulas, but on a few i'm not sure how to begin. I'd appreciate any help. Thanks!

1. Find (lim x-->pi/2) sin(14x)/sin(7x)

2. Find f' for f(x) = (3+4cos(x))/(4+5sin(x))

3. Find (lim x-->0) (sin³(2t))/(tan²(3t))

sorry for any formatting issues. Thanks again for any help!

 

[HallsofIvy]

hello, i'm just looking for help with a few problems involving trig function derivatives. I know the formulas, but on a few i'm not sure how to begin. I'd appreciate any help. Thanks!

1. Find (lim x-->pi/2) sin(14x)/sin(7x)

If a function, f, is continuous at x= a, \(\displaystyle \lim_{x\to a} f(x)= f(a). sin(x) is continuous for all x and a fraction of functions is continuous as long as the denominator is not 0.

2. Find f' for f(x) = (3+4cos(x))/(4+5sin(x))

Do you know the "quotient law"? What do you get when you use that?

3. Find (lim x-->0) (sin³(2t))/(tan²(3t))

Write tan(3t) as sin(3t)/cos(3t) and separate into "sine" and "cosine" fractions.
Alternatively, use "L'Hopital's rule" to reduce the limit.

sorry for any formatting issues. Thanks again for any help!

\)