anonymous
  • anonymous
Help with trig limit question!!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
lim as x -> 0 for the function (cos(7 theta) * tan(7 theta)) / theta
anonymous
  • anonymous
using u substitution i just replace the (7 theta) with u and simplify to sin(u)/theta
anonymous
  • anonymous
which would be sin(7 theta) / theta

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anonymous
  • 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
anonymous
  • anonymous
\[\lim_{\theta \rightarrow 0}\frac{ \cos 7\theta \tan 7\theta }{ \theta}\] \[=\lim_{\theta \rightarrow 0}\frac{ \sin 7\theta }{ 7\theta } \times 7=7*1=7\]
anonymous
  • anonymous
ok where did the 7 come from on the bottom?
anonymous
  • anonymous
to make \[\frac{ \sin x }{ x }\] multiply the numerator and denominator by 7
anonymous
  • anonymous
wouldn't it be \[\frac{ \sin7\theta }{ \theta } * 7\]
anonymous
  • anonymous
whatever with sin ,same is denominator
anonymous
  • anonymous
\[\frac{ \sin 7\theta }{ \theta }\times \frac{ 7 }{ 7 }=\frac{ 7*\sin 7\theta }{ 7\theta }\]
anonymous
  • anonymous
ok so how does that solve the problem with 7 theta?
anonymous
  • anonymous
what would cancel with the 7 theta on the bottom is my real question
anonymous
  • anonymous
|dw:1440738190981:dw| we multiplied by 1= 7/7
anonymous
  • anonymous
ok i think im missing something here because that would be 1/0 = undefined
anonymous
  • anonymous
sin of zero = 1 and 7 * 0 = 0 so that would be 1/0
anonymous
  • anonymous
wanted to clarify i just saw a mistake in how i presented the question it should say lim -> theta instead of lim -> x
IrishBoy123
  • 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
anonymous
  • anonymous
oh ok wow i can't believe i didn't catch that, now it makes alot of sense

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