# Evaluate the limit

• Nov 22nd 2009, 07:18 PM
Johnny Walker Black
Evaluate the limit
http://i754.photobucket.com/albums/x...Picture2-1.png
Question 2 the limit of (1-cos(x))/(x^2) as x approaches 0. i applied l'Hospitals rule twice and came up with -1/2 my professor got positive 1/2 help me out.
-i know it has the form 0/0.
-after i applied LH rule the 1st time i got (0+1sinx)/(2x)
-LH applied twice i got (-cos(x))/(2) = -1/2

http://i754.photobucket.com/albums/x...Picture1-2.png

Also this problem has been troubling me is there a formula that could help me out? thanks everyone.
• Nov 22nd 2009, 07:24 PM
tonio
Quote:

Originally Posted by Johnny Walker Black
http://i754.photobucket.com/albums/x...Picture2-1.png
Question 2 the limit of (1-cos(x))/(x^2) as x approaches 0. i applied l'Hospitals rule twice and came up with -1/2 my professor got positive 1/2 help me out.
-i know it has the form 0/0.
-after i applied LH rule the 1st time i got (0+1sinx)/(2x)
-LH applied twice i got (-cos(x))/(2) = -1/2

The derivative of $\sin x$ is $\cos x$ , with a positive sign, not negative.

http://i754.photobucket.com/albums/x...Picture1-2.png

Also this problem has been troubling me is there a formula that could help me out? thanks everyone.

The formula for velocity depending on constant acceleration (gravity's) and initial velocity, which I don't remember right now (I'm a mathematician, not a physicist), but it looks something like $v=v_0+at$ , or stuff.

Tonio