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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lim as x > 0 for the function (cos(7 theta) * tan(7 theta)) / theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0using u substitution i just replace the (7 theta) with u and simplify to sin(u)/theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which would be sin(7 theta) / theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{\theta \rightarrow 0}\frac{ \cos 7\theta \tan 7\theta }{ \theta}\] \[=\lim_{\theta \rightarrow 0}\frac{ \sin 7\theta }{ 7\theta } \times 7=7*1=7\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok where did the 7 come from on the bottom?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to make \[\frac{ \sin x }{ x }\] multiply the numerator and denominator by 7

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't it be \[\frac{ \sin7\theta }{ \theta } * 7\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0whatever with sin ,same is denominator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ \sin 7\theta }{ \theta }\times \frac{ 7 }{ 7 }=\frac{ 7*\sin 7\theta }{ 7\theta }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so how does that solve the problem with 7 theta?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what would cancel with the 7 theta on the bottom is my real question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440738190981:dw we multiplied by 1= 7/7

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i think im missing something here because that would be 1/0 = undefined

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sin of zero = 1 and 7 * 0 = 0 so that would be 1/0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wanted to clarify i just saw a mistake in how i presented the question it should say lim > theta instead of lim > x

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[\lim_{ \theta > 0} \ \frac{cos(7 \theta) \ tan(7 \theta) }{ \theta} \\ = \lim_{ \theta > 0} \ \frac{sin(7 \theta) }{ \theta} \\ = \lim_{ u > 0} \ \frac{sin(u) }{ \ \frac{u}{7}} \\ = 7 \lim_{ u > 0} \frac{sinu}{u} \\ = 7\] which only restates what @surjithayer said

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok wow i can't believe i didn't catch that, now it makes alot of sense
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