Proof of: limq?0 (cosq -1)/q = 0 trig limit, Mathematics

Proof of: limq→0 (cosq -1)/q = 0

We will begin by doing the following,

limq→0 (cosq -1)/q = limq→0((cosq - 1)(cosq + 1))/(q (cosq + 1))

= limq→0(cos2q - 1)/ (q (cosq + 1))                                           (7)

Here, let's recall that,

cos2q + sin2q = 1      =>   cos2q - 1 = -sin2q

By using this in (7) provides us,

= limq→0(sin2q)/ (q (cosq + 1))

= limq→0 (sinq/q)(-sinq)/(cosq + 1)

= limq→0 (sinq/q)  limq→0 (-sinq)/(cosq + 1)

Here, as we just proved the first limit and the second can be got directly we are pretty much done.  All we require to do is get the limits.

limq→0 cosq - 1

= limq→0 (sinq/q)  limq→0 (-sinq)/(cosq + 1)

= (1) (0)

 = 0

Posted Date: 4/13/2013 3:52:18 AM | Location : United States







Related Discussions:- Proof of: limq?0 (cosq -1)/q = 0 trig limit, Assignment Help, Ask Question on Proof of: limq?0 (cosq -1)/q = 0 trig limit, Get Answer, Expert's Help, Proof of: limq?0 (cosq -1)/q = 0 trig limit Discussions

Write discussion on Proof of: limq?0 (cosq -1)/q = 0 trig limit
Your posts are moderated
Related Questions
I need help solving principal equations where interest,rate,and time are given.

What is the slowest a boat can travel across a river if the river is flowing with a velocity field of X^2?


Newton's Method : If x n is an approximation a solution of f ( x ) = 0 and if given by, f ′ ( x n ) ≠ 0 the next approximation is given by




different kind of ellipsoid

Can you explain that a wave through the origin always has a slope of one or not?

A regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual