Question

Help with trig limit question!!!

Answer 1

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

Answer 2

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

Answer 3

which would be sin(7 theta) / theta

Answer 4

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

Answer 5

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

Answer 6

ok where did the 7 come from on the bottom?

Answer 7

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

Answer 8

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

Answer 9

whatever with sin ,same is denominator

Answer 10

\[\frac{ \sin 7\theta }{ \theta }\times \frac{ 7 }{ 7 }=\frac{ 7*\sin 7\theta }{ 7\theta }\]

Answer 11

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

Answer 12

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

Answer 13

we multiplied by 1= 7/7

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

\[\lim_{ \theta -> 0} \ \frac{cos(7 \theta) \ tan(7 \theta) }{ \theta} \\ = \lim_{ \theta -> 0} \ \frac{sin(7 \theta) }{ \theta} \\ = \lim_{ u -> 0} \ \frac{sin(u) }{ \ \frac{u}{7}} \\ = 7 \lim_{ u -> 0} \frac{sinu}{u} \\ = 7\]

which only restates what @surjithayer said

Answer 18

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