Thread: limits problems--need help!

I'm stuck on getting the limits for sin/cos problems... mind helping me solve these problems?

1. lim x-->0 x^2/1-cosx
2. lim x-->0 x/sin3x
3. lim x-->0 sin5x/sin2x

(I don't know how to type limit problems in this forum..)

Are you allowed to use L'Hospital's Rule? If so,







You can use the same approach for the other two problems.

Originally Posted by kdl00

I'm stuck on getting the limits for sin/cos problems... mind helping me solve these problems?

1. lim x-->0 x^2/1-cosx
2. lim x-->0 x/sin3x
3. lim x-->0 sin5x/sin2x

(I don't know how to type limit problems in this forum..)

Neither do I. But I can help you.

Use L'hopital's Rule. If you have a limit that approaches 0, the function is a fraction, and the solution comes out undefined, get the derivative of the numerator, and the derivative of the denominator, and you should be able to solve it. I'll do number one:

lim x-->0 x^2/1-cosx

becomes:

lim x-->0 2x/sinx

becomes:

lim x-->0 2/cosx

becomes:

2/1

and you can repeat it as much as you like as long as the limit approaches zero.

Originally Posted by kdl00

I'm stuck on getting the limits for sin/cos problems... mind helping me solve these problems?

1. lim x-->0 x^2/1-cosx
2. lim x-->0 x/sin3x
3. lim x-->0 sin5x/sin2x

(I don't know how to type limit problems in this forum..)

1. Either use l'Hopital's Rule or substitute the Maclaurin series for cos x and simplify. Or use a useful trig limit found here: World Web Math: Useful Trig Limits

2. Note that it can be writen as . Now use a useful trig limit.

3. Note that it can be written as . Now use a useful trig limit.