Find limits of sine and cosine functions

[Glissando]

Homework Statement

Find the limit:

lim (1-cos2x)/(xsinx)
x->0

Homework Equations

Identities

The Attempt at a Solution

I've done this over and over and over again! The answer is supposed to be 0 but I keep getting 2 ):

lim (1-cos2x)/(xsinx)
x->0

lim (1-1+2sin²x)/(xsinx)
x->0

lim (2sin²x)/(xsinx)
x->0

lim (2sinx)/x
x->0

= 2*1 = 2

Any help is appreciated! Thank you!

 

[micromass]

Hi Glissando!

In fact, 2 is the correct answer. Look at http://www.wolframalpha.com/input/?i=(1-cos(2x))/(x*sin(x))"

Who says the answer is supposed to be 0?

 

[Dick]

I don't see anything wrong with what you did. I'd say the limit is 2 as well.

 

[Glissando]

Thanks guys (: I guess textbook error then! Yay!

Thank you <3