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Math Help - Tough Possibly Long Cal I problem need help

  1. #1
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    Tough Possibly Long Cal I problem need help

    Estimate f(0.009) if f(x)=sin(sin(sin(5x)))/cos(sin(x)).
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  2. #2
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    You could try f(x+h)\approx f(x)+h\times f'(x)
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  3. #3
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    what is that? limit definition?
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  4. #4
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    No its a first order approximation.

    It can estimate an answer for you.
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  5. #5
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    can u give an example of a problem using that formula i dunno how to use it?
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  6. #6
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    does this problem have anything to do with Trigonometric Functions or inverse Trigonometric Functions?
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  7. #7
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    Quote Originally Posted by Fyou88 View Post
    can u give an example of a problem using that formula i dunno how to use it?
    Estimate f(0.5) where f(x) = \sin x

    f(x+h)\approx f(x)+h\times f'(x)

    f(x) = \sin x \implies f'(x) = \cos x

    f(x+h)\approx \sin x+h\times \cos x

    Using f(0.5) = f(0+0.5) i.e x = 0,h=0.5

    f(0+0.5)\approx \sin 0+0.5 \times \cos 0

    f(0+0.5)\approx 0+0.5 \times 1 = 0.5
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  8. #8
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    wow so means i have to find the derivative of sin(sin(sin(5x)))/cos(sin(x))? to get slope? and i would need chain rule??
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