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Math Help - Please help with calculus problems..

  1. #1
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    Post Please help with calculus problems..

    1. If an arrow is shot straight upward on the moon with a velocity of 78 m/s, its height (in meters) after t seconds is given by .
    What is the velocity of the arrow (in m/s) after 7 seconds? 66.38 m/s

    After how many seconds will the arrow hit the moon? 94 seconds
    With what velocity (in m/s) will the arrow hit the moon? How do you find this?? Is it 78 m/s?

    2. If
    find the values of and that make differentiable everywhere.
    Find m=? and b=?

    3. Given that


    Calculate 6
    Calculate -8
    Calculate ( -7)
    Calculate (-1/7)
    Both answers for (f*g) and (f/g) are wrong...does anyone know why?
    Last edited by Kayla_N; February 23rd 2009 at 12:12 PM.
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  2. #2
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    Quote Originally Posted by Kayla_N View Post
    3. Given that



    Calculate 6
    Calculate -8
    Calculate i cant figure this out??
    Calculate This one too?
    Calculate i cant figure this out??
    f'(3)*g'(3) = (-1*7)=-7

    Calculate This one too?
    f'(3)/g'(3) = (-1/7)= -\frac 1 7
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  3. #3
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    I got that answer too..but its not right. I dont understand what they looking for??
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  4. #4
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    With what velocity (in m/s) will the arrow hit the moon? How do you find this?? Is it 78 m/s?
    velocity is the derivative of position ...

    v(t) = 78 - 1.66t

    2. If
    find the values of and that make differentiable everywhere.
    Find m=? and b=?
    function needs to be continuous ...
    f(10) = 100 , so 100 = m(10) + b

    to be differentiable ...
    f'(10) = 20, so 20 = m ... b = -100



    Both answers for (f*g) and (f/g) are wrong...does anyone know why?
    product rule ...

    (f \cdot g)'(x) = f(x) \cdot g'(x) + g(x) \cdot f'(x) <br />

    quotient rule ...

    \left(\frac{f}{g}\right)'(x) = \frac{g(x) \cdot f'(x) - f(x) \cdot g'(x)}{[g(x)]^2}
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  5. #5
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    Quote Originally Posted by skeeter View Post

    function needs to be continuous ...
    f(10) = 100 , so 100 = m(10) + b

    to be differentiable ...
    f'(10) = 20, so 20 = m ... b = -100
    It's actually differentiable to be continuous.
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  6. #6
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    Quote Originally Posted by Krizalid View Post
    It's actually differentiable to be continuous.
    I agree ... I did not mean that as a continued statement.

    It's just easier to start with continuity when trying to determine m and b.
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  7. #7
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    Well thank you very much skeeter. That was really helpful and I appreciated.
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