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iop360

  • 3 years ago

find the slope of the line tangent to the following curve where x = 1...

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  1. iop360
    • 3 years ago
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    \[y = \sin[x - \tan (\frac{ \Pi }{ 4 }x^{66})] + x ^{\frac{ 1 }{ 1 + 66\Pi }}\]

  2. iop360
    • 3 years ago
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    if you cant see the exponent part at the end, its: \[\frac{ 1 }{ 1+66\Pi }\]

  3. iop360
    • 3 years ago
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    answer is -99Pi

  4. iop360
    • 3 years ago
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    im currently at this step: \[\frac{ -66\Pi }{ 4} + \frac{ 1 }{ 1 + 66\Pi }\]

  5. zepdrix
    • 3 years ago
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    Oh goodness.. this one again iop? XD

  6. iop360
    • 3 years ago
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    heh

  7. zepdrix
    • 3 years ago
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    Hmm

  8. zepdrix
    • 3 years ago
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    What is that symbol? Is that suppose to be pi?

  9. iop360
    • 3 years ago
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    yes

  10. zepdrix
    • 3 years ago
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    Why don't u use lowercase? D: that's so confusing..

  11. iop360
    • 3 years ago
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    i was wondering if that was confusing people

  12. iop360
    • 3 years ago
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    i guess so

  13. zepdrix
    • 3 years ago
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    Hmm you sure the step you got to is correct so far? :O

  14. iop360
    • 3 years ago
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    i got this for y prime: \[y' = \cos[x - \tan(\frac{ \pi }{ 4 }x^{66})](1 - \sec^2(\frac{ \pi }{ 4 }x^{66}))(\frac{ 66\pi }{ 4 }x^{65}) + \frac{ 1 }{ 1+66\pi }x^\frac{ 1 }{ 1+66\pi }-1\]

  15. zepdrix
    • 3 years ago
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    So what i tried to do is... After you get a common denominator and all that jazz.. you have something that looks like a polynomial in the numerator. And I'm not seeing it factor nicely :( at least not in any way that will cancel with the denominator. Hmmm

  16. iop360
    • 3 years ago
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    plugged 1 in.. \[y'(1) = 1(-1)(\frac{ 66\pi }{ 4 })(\frac{ 1 }{ 1+ 66\pi })\]

  17. iop360
    • 3 years ago
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    lol

  18. iop360
    • 3 years ago
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    the factoring is the confusing part... how am i supposed to get it to -99pi

  19. iop360
    • 3 years ago
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    unless the steps i did to get it to that point were incorrect...i dont think so

  20. zepdrix
    • 3 years ago
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    |dw:1349581968847:dw| Hmm yah your steps look good so far :o

  21. iop360
    • 3 years ago
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    yep

  22. zepdrix
    • 3 years ago
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    Oh that last term should be addition.. my bad. The way that you have it originally wrote out.

  23. iop360
    • 3 years ago
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    yea

  24. zepdrix
    • 3 years ago
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    |dw:1349582282567:dw| Hmmmm...

  25. iop360
    • 3 years ago
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    yes! i did that, now im stuck..

  26. iop360
    • 3 years ago
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    some kind of factorization trick in there, perhaps?

  27. zepdrix
    • 3 years ago
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    Mmmm I don't see one :\ Must be something else going on there. Blah I give up! XD

  28. iop360
    • 3 years ago
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    thanks anyway

  29. micahwood50
    • 3 years ago
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    What the **** kind of teacher give you question like that?!? Or did you make up this question on your own?

  30. iop360
    • 3 years ago
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    online homework haha

  31. iop360
    • 3 years ago
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    |dw:1349583464134:dw|

  32. iop360
    • 3 years ago
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    the 4's cancel out..but then what? lol

  33. iop360
    • 3 years ago
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    i guess the neg sign could be the neg sign in the answer: -99pi

  34. zepdrix
    • 3 years ago
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    What we currently have = -51.83147906... -99pi = -311.0176727 Hmmm something isn't right, that doesn't equal -99pi

  35. iop360
    • 3 years ago
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    yes that too

  36. iop360
    • 3 years ago
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    i guess i could submit this answer wrong and get a similar question with different values

  37. iop360
    • 3 years ago
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    or that could make things worse

  38. micahwood50
    • 3 years ago
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    According to WolframAlpha, the answer is -102.68 or \[1-33 \pi+\frac{1}{1+66 \pi}\] http://www.wolframalpha.com/input/?i=derivative+of++sin%28x+-+tan%28pi+%2F+4+x%5E66%29%29+%2B+x%5E%28%281%29%2F%281%2B66+pi%29%29+when+x+%3D+1

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