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v.s

  • 2 years ago

Find the limit. lim 3 − 3 tan x/sin x − cos x x→π/4

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  1. zordoloom
    • 2 years ago
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    Could you write out how this looks. the division sign doesn't really indicate where the equation is divided.

  2. zordoloom
    • 2 years ago
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    At least put parenthesis where they belong.

  3. v.s
    • 2 years ago
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    lim (3 − 3 tan x)/(sin x − cos x) x→π/4

  4. frx
    • 2 years ago
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    First try to just put in the value pi/4 and decide if the function is defined in that point

  5. zordoloom
    • 2 years ago
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    you'll get -3sqrt(2)

  6. frx
    • 2 years ago
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    You see that sin pi/4- cos pi/4 equals zero so the function is undefined at pi/4 so what you want to do is to simplify the function

  7. v.s
    • 2 years ago
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    okaaaaaaaaay thambi

  8. v.s
    • 2 years ago
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    how do i simplify this?

  9. chrisplusian
    • 2 years ago
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    you can turn your denominator into\[(3-3(\frac{ cosx }{ sinx })\] then split the numerator into two different fractions\[\frac{ 3 }{ sinx-cosx } - \frac{ \frac{ sinx }{ cosx } }{ sinx-cosx }\]

  10. chrisplusian
    • 2 years ago
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    sorry meant numerator

  11. chrisplusian
    • 2 years ago
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    and that should have been three times sine over cosine sorry I am messing it up pretty bad

  12. v.s
    • 2 years ago
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    loll itss okayy

  13. v.s
    • 2 years ago
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    i dont get the question

  14. Coolsector
    • 2 years ago
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    \[\frac{ 3-3\tan(x) }{ \sin(x) - \cos(x) } \times \frac{ \sin(x) +\cos(x) }{ \sin(x) +\cos(x) }\]

  15. Coolsector
    • 2 years ago
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    \[\frac{ 3\sin(x) - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) -3\sin(x) }{ \sin^2(x) -\cos^2(x) }\]

  16. Coolsector
    • 2 years ago
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    \[\frac{ - 3\frac{ \sin^2(x) }{ \cos(x) } + 3\cos(x) }{ \sin^2(x) -\cos^2(x) }\]

  17. Coolsector
    • 2 years ago
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    \[\frac{ - 3\sin^2(x) + 3\cos^2(x) }{ \cos(x)[\sin^2(x) -\cos^2(x)] } = \frac{ -3 }{ \cos(x) }\]

  18. v.s
    • 2 years ago
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    sorry i was busy

  19. v.s
    • 2 years ago
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    so i sub in pi/4

  20. Coolsector
    • 2 years ago
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    yes

  21. v.s
    • 2 years ago
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    -3/(1/sqroot2)

  22. Coolsector
    • 2 years ago
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    which simplifies into -3sqrt(2)

  23. v.s
    • 2 years ago
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    -sqroot2/3

  24. Coolsector
    • 2 years ago
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    no .. -3 * sqrt(2)

  25. v.s
    • 2 years ago
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    yeye

  26. v.s
    • 2 years ago
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    i gett it

  27. Coolsector
    • 2 years ago
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    \[-3\sqrt2\]

  28. Coolsector
    • 2 years ago
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    like this

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