Name: Anonymous 2007-05-29 20:40 ID:/lIhdw7k
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?
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?