Limits and trigonometry

Okay. So I have this homework problem here and I can't really figure out how to do it. The problem is...

The limit of sin(2x)/x as x approaches 0.

I know how to do it using my TI-83, but I'm supposed to be able to do it by hand using these four facts:

The limit of sin(x)/x as x approaches zero = 1
The limit of (cos(x)-1)/x as x approaches zero = 0
The limit of sin(x) as x approaches zero = 0
The limit of cos(x) as x approaches zero = 1

I've tried rewriting it using the double angle formula thing to get...

(2sin(x)cos(x))/x

Which I tried rewriting as (2/x)+(sin(x)/x)+(cos(x)/x)

But then I get all confused and I don't know what to do. Help?

squeeze theorem

Uh...
What?
I looked it up on wikipedia, and I understand what it is, but I have no clue how to apply it to this. And I'm sure we don't have to use it because we haven't learned it at all yet.

The limit is 2.

How about this argument:

lim x->0 Sin(2x)/x
= lim x->0 2Cos(2x) (by L'Hopital's rule)
= (lim x->0 2)(lim x->0 Re(e^(2ix))) (where Re(z) denotes the real part of z and e is the base of the natural log)
= 2(lim x->0 Cos(x)^2 - Sin(x)^2)
= 2((lim x->0 Cos(x))^2 - (lim x->0 Sin(x))^2)
= 2((1)^2 - (0)^2)
= 2

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The limit of sin(2x)/2x as x goes to 0 is 1, which can easily be seen from the first fact you're given. sin(2x)/x = 2 * sin(2x)/2x, so the limit as x goes to 0 of sin(2x)/x is equal to 2.

if x on the bottom have to divide by zero and u cant so trick question cant answer this or id say 0

>>7
oy..

(2sin(x)cos(x))/x
=(2/x)+(sin(x)/x)+(cos(x)/x)

lol wut?

>>7

L'HOPITAL'S RULE, BOY.

lim    sin(2x)/x
x->0

= lim    (2cos(2x))/1
  x->0

= 2

Read the post guys, he is not allowed to use L'Hopital.  >>6 has the right answer.

>>6
Why thank you. That's perfect.

"Which I tried rewriting as (2/x)+(sin(x)/x)+(cos(x)/x)"
phail

You can still solve the question with the double angle method you wrote: (2sin(x)cos(x))/x = 2cos(x)[sin(x)/x] = 2*1*1 = 2

>>2 is unrelated, and >>6 has a valid answer.

suck me until my vas deferens gives out

fucking asians only board

hi maths forum

Divide by zero. Oh shi-

The word pirahna, is all I can think of that rhymes with marijuana

Marijuana MUST be legalized.