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anonymous

  • one year ago

Help with trig limit question!!!

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  1. anonymous
    • one year ago
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    lim as x -> 0 for the function (cos(7 theta) * tan(7 theta)) / theta

  2. anonymous
    • one year ago
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    using u substitution i just replace the (7 theta) with u and simplify to sin(u)/theta

  3. anonymous
    • one year ago
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    which would be sin(7 theta) / theta

  4. anonymous
    • one year ago
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    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
    • one year ago
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    \[\lim_{\theta \rightarrow 0}\frac{ \cos 7\theta \tan 7\theta }{ \theta}\] \[=\lim_{\theta \rightarrow 0}\frac{ \sin 7\theta }{ 7\theta } \times 7=7*1=7\]

  6. anonymous
    • one year ago
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    ok where did the 7 come from on the bottom?

  7. anonymous
    • one year ago
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    to make \[\frac{ \sin x }{ x }\] multiply the numerator and denominator by 7

  8. anonymous
    • one year ago
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    wouldn't it be \[\frac{ \sin7\theta }{ \theta } * 7\]

  9. anonymous
    • one year ago
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    whatever with sin ,same is denominator

  10. anonymous
    • one year ago
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    \[\frac{ \sin 7\theta }{ \theta }\times \frac{ 7 }{ 7 }=\frac{ 7*\sin 7\theta }{ 7\theta }\]

  11. anonymous
    • one year ago
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    ok so how does that solve the problem with 7 theta?

  12. anonymous
    • one year ago
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    what would cancel with the 7 theta on the bottom is my real question

  13. anonymous
    • one year ago
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    |dw:1440738190981:dw| we multiplied by 1= 7/7

  14. anonymous
    • one year ago
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    ok i think im missing something here because that would be 1/0 = undefined

  15. anonymous
    • one year ago
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    sin of zero = 1 and 7 * 0 = 0 so that would be 1/0

  16. anonymous
    • one year ago
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    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
    • one year ago
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    \[\lim_{ \theta -> 0} \ \frac{cos(7 \theta) \ tan(7 \theta) }{ \theta} \\ = \lim_{ \theta -> 0} \ \frac{sin(7 \theta) }{ \theta} \\ = \lim_{ u -> 0} \ \frac{sin(u) }{ \ \frac{u}{7}} \\ = 7 \lim_{ u -> 0} \frac{sinu}{u} \\ = 7\] which only restates what @surjithayer said

  18. anonymous
    • one year ago
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    oh ok wow i can't believe i didn't catch that, now it makes alot of sense

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