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anonymous

  • 5 years ago

find the linear approximation L(x) of the function f(x)=cos(9x) at a=pi/2 is L(x)=A+Bx

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  1. bahrom7893
    • 5 years ago
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    okay workin on it

  2. bahrom7893
    • 5 years ago
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    L(x) = f(a) + f'(a)(x - a)

  3. bahrom7893
    • 5 years ago
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    f'(x) = -Sin(9x) * 9

  4. bahrom7893
    • 5 years ago
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    f'(pi/2) = -9Sin(9pi/2) = -9*1 = -9

  5. bahrom7893
    • 5 years ago
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    And f(pi/2) = Cos(9pi/2) = 0

  6. anonymous
    • 5 years ago
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    ok whats A and what B

  7. bahrom7893
    • 5 years ago
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    L(x) = 0 - 9(x-pi/2) L(x) = A + Bx (<--was this right, i keep forgetting the format?)

  8. anonymous
    • 5 years ago
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    yes but i do not know how u got ur answer at all

  9. bahrom7893
    • 5 years ago
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    Oh okay so let me explain... L(x) = f(a) + f'(a)(x - a) <-Linear approximation formula

  10. anonymous
    • 5 years ago
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    i got that

  11. bahrom7893
    • 5 years ago
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    Now for that you are going to need: f(a), f'(a) and x-a

  12. bahrom7893
    • 5 years ago
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    f(a) = f(pi/2)

  13. bahrom7893
    • 5 years ago
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    f(pi/2)=cos(9[pi/2]) = 0

  14. anonymous
    • 5 years ago
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    i got that the cos (9pi/2)= a decimal

  15. bahrom7893
    • 5 years ago
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    what is ur calculator's mode in? I bet it's in degrees.. supposed to be in radians

  16. bahrom7893
    • 5 years ago
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    pi/2 is a radian measure, not degree measure..

  17. bahrom7893
    • 5 years ago
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    try again? change the mode and find Cos(9pi/2)

  18. anonymous
    • 5 years ago
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    i am in radians

  19. bahrom7893
    • 5 years ago
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    okay can u go to mode and type in the values u have in here?

  20. anonymous
    • 5 years ago
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    dont kno how

  21. bahrom7893
    • 5 years ago
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    what calculator are u using?

  22. anonymous
    • 5 years ago
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    ti 83

  23. bahrom7893
    • 5 years ago
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    okay press MODE

  24. bahrom7893
    • 5 years ago
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    now type whatever u see in that screen here

  25. bahrom7893
    • 5 years ago
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    MODE is right next to 2nd key

  26. anonymous
    • 5 years ago
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    i see stuff like normal Sci Eng FLoat 0123456789 Radia Degree Func PAr Pol Seq

  27. bahrom7893
    • 5 years ago
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    what are the values, wait nevermind, can u take a picture of that mode screen and upload it on tinypic.com ? no registration needed btw

  28. anonymous
    • 5 years ago
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    dont know how to do that either

  29. bahrom7893
    • 5 years ago
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    do u have a camera?

  30. bahrom7893
    • 5 years ago
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    wait nevermind, trust me Cos(9pi/2) is 0

  31. bahrom7893
    • 5 years ago
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    okay?

  32. anonymous
    • 5 years ago
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    ok

  33. bahrom7893
    • 5 years ago
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    L(x) = f(a) + f'(a)(x - a) <-Linear approximation formula f(a) = f(pi/2) f(pi/2)=cos(9[pi/2]) = 0

  34. anonymous
    • 5 years ago
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    ok

  35. bahrom7893
    • 5 years ago
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    f'(x) = [cos(9x)]' = USE CHAIN RULE = -Sin(9x) * 9 = -9Sin(9x)

  36. bahrom7893
    • 5 years ago
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    f'(pi/2) = -9 Sin(9pi/2) = -9 * 1 = -9

  37. bahrom7893
    • 5 years ago
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    L(x) = f(a) + f'(a)(x - a) <-Linear approximation formula f(a) = f(pi/2) f(pi/2)=cos(9[pi/2]) = 0 f'(pi/2) = -9 Sin(9pi/2) = -9 * 1 = -9 L(x) = f(a) + f'(a)(x - a) L(pi/2) = 0 + -9 (x - pi/2)

  38. bahrom7893
    • 5 years ago
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    L(pi/2) = -9x - 9pi/2

  39. bahrom7893
    • 5 years ago
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    L(pi/2) = -9x - 9pi/2 L(x) = A + Bx L(pi/2) = -9pi/2 - 9x

  40. bahrom7893
    • 5 years ago
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    A = -9pi/2 B = -9

  41. bahrom7893
    • 5 years ago
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    Check the answer

  42. bahrom7893
    • 5 years ago
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    carra u here? I made a mistake, -9 (x - pi/2) is not -9pi/2 - 9x, its 9pi/2 - 9x

  43. bahrom7893
    • 5 years ago
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    Double negative is a positive... -9 * -pi/2 is 9pi/2 not -9pi/2

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