anonymous one year ago Help with trig limit question!!!

1. anonymous

lim as x -> 0 for the function (cos(7 theta) * tan(7 theta)) / theta

2. anonymous

using u substitution i just replace the (7 theta) with u and simplify to sin(u)/theta

3. anonymous

which would be sin(7 theta) / theta

4. anonymous

im not quite sure what im supposed to do after this point and multiplying the top and the bottom by theta doesn't seem like it helps much

5. anonymous

$\lim_{\theta \rightarrow 0}\frac{ \cos 7\theta \tan 7\theta }{ \theta}$ $=\lim_{\theta \rightarrow 0}\frac{ \sin 7\theta }{ 7\theta } \times 7=7*1=7$

6. anonymous

ok where did the 7 come from on the bottom?

7. anonymous

to make $\frac{ \sin x }{ x }$ multiply the numerator and denominator by 7

8. anonymous

wouldn't it be $\frac{ \sin7\theta }{ \theta } * 7$

9. anonymous

whatever with sin ,same is denominator

10. anonymous

$\frac{ \sin 7\theta }{ \theta }\times \frac{ 7 }{ 7 }=\frac{ 7*\sin 7\theta }{ 7\theta }$

11. anonymous

ok so how does that solve the problem with 7 theta?

12. anonymous

what would cancel with the 7 theta on the bottom is my real question

13. anonymous

|dw:1440738190981:dw| we multiplied by 1= 7/7

14. anonymous

ok i think im missing something here because that would be 1/0 = undefined

15. anonymous

sin of zero = 1 and 7 * 0 = 0 so that would be 1/0

16. anonymous

wanted to clarify i just saw a mistake in how i presented the question it should say lim -> theta instead of lim -> x

17. IrishBoy123

$\lim_{ \theta -> 0} \ \frac{cos(7 \theta) \ tan(7 \theta) }{ \theta} \\ = \lim_{ \theta -> 0} \ \frac{sin(7 \theta) }{ \theta} \\ = \lim_{ u -> 0} \ \frac{sin(u) }{ \ \frac{u}{7}} \\ = 7 \lim_{ u -> 0} \frac{sinu}{u} \\ = 7$ which only restates what @surjithayer said

18. anonymous

oh ok wow i can't believe i didn't catch that, now it makes alot of sense