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
what is actual error and how do you calculate percentage error

find the volume of a rectangular based right pyramid with its base 18 cm by 24 cm and the slanted edge 39 cm

Evaluate following sin 2 ?/3   and sin (-2 ?/3) Solution: The first evaluation in this part uses the angle 2 ?/3.  It is not on our unit circle above, though notice that  2 ?/


I need help converting my project fractions into 1

the automatic hopper loader is set to put 36 tons of coal in each car. the actual weights of coal loaded into each car arw normally distributed with a mean of 36 tons and a standar

Five years ago a business borrowed $100,000 agreeing to repay the principal and all accumulated interest at 8% pa compounded quarterly, 8 years from the loan date. Two years after

What is the greatest common factor of 24 and 64? List the factors of 24 and 64. The largest factor that they have in common is the greatest common factor. Factors of 24: 1,


If  the  ratios  of  the  polynomial ax 3 +3bx 2 +3cx+d  are  in  AP,  Prove  that  2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z