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
If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value(s) of k..

Jake required to find out the perimeter of an equilateral triangle whose sides measure x + 4 cm each. Jake realized that he could multiply 3 (x + 4) = 3x + 12 to find out the total

It is the catch all force. If there are some other forces which we decide we need to act on our object we lump them in now and call this good. We classically call F(t) the forcing

mean absolue deviation

How can I submit a sample of my work in either teaching online or checking homework as I am retired and doing this for the first time?

the area of a triangle is 20 and its base is 16. Find the base of a similar triangle whose area is 45. Given is a regular pentagon. Find the measure of angle LHIK.


Children Have Their Own Strategies For Learning Vibhor, aged 7, was once asked if he knew what 'seven lots of eight' are. He said he didn't. He was then asked, "Can you work it

assignment of mathematics in b.sc. 1sem

we know that    A^m/A^m=1                    so A^(m-m)=1                    so A^0=1.....