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Math Help - Continuity of hybrid functions.

  1. #1
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    Continuity of hybrid functions.

    Final is tomorrow brahs....I NEED an A.

    I just Don't understand the steps to solving these, please show step by step what you do.







    For this last one I get 5sin^4 (x^3 +3)+sin^5 (3x^2)

    But he says the right answer is: 5sin^4 (x^3)cos(x^3 +3)(3x^2)

    Where do you get that cos?
    Last edited by mr fantastic; July 25th 2011 at 07:28 PM. Reason: Title.
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  2. #2
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    Re: Need some Calc 1 Help PLEASE!

    Hi Bespetna, your hyperlinks are broken on my machine.
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  3. #3
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    Re: Need some Calc 1 Help PLEASE!

    Quote Originally Posted by pickslides View Post
    Hi Bespetna, your hyperlinks are broken on my machine.
    http://i200.photobucket.com/albums/a...725_181552.jpg

    http://i200.photobucket.com/albums/a...725_181609.jpg

    http://i200.photobucket.com/albums/a...725_185540.jpg

    I just thought showing you direct pictures of the questions would be easier for someone to understand.

    Please tell me if these links do not work and i can just write down the questions
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    Re: Need some Calc 1 Help PLEASE!

    Quote Originally Posted by Bespetna View Post

    Please tell me if these links do not work and i can just write down the questions
    It's always best to write down the questions here.

    Be sure to show your workings and where you are stuck.
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  5. #5
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    Re: Need some Calc 1 Help PLEASE!

    1) Let f(x)=A^2 X^2, X <or equal to 2
    (1-A)x, x>2

    For what values of A is f continuous at X=2

    2) Is the following function continuous at X=3?
    Redefine it so that it is continuous? Let
    f(x) = (x^2-x-6)/(x-3) X does not equal 3
    8 x=3
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    Re: Need some Calc 1 Help PLEASE!

    3)
    Find the derivative of f(x)=sin^5 (x^3+3)

    For this last one I get 5sin^4 (x^3 +3)+sin^5 (3x^2)

    But he says the right answer is: 5sin^4 (x^3)cos(x^3 +3)(3x^2)
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  7. #7
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    Re: Need some Calc 1 Help PLEASE!

    Quote Originally Posted by Bespetna View Post
    1) Let f(x)=A^2 X^2, X <or equal to 2
    (1-A)x, x>2
    The first function is a parabola and the second a linear function, the entire function will be continuous at x=2 if they are equal there.

    So solve a^2\times 2^2 = (1-a)\times 2



    Quote Originally Posted by Bespetna View Post
    2) Is the following function continuous at X=3?
    Redefine it so that it is continuous? Let
    f(x) = (x^2-x-6)/(x-3) X does not equal 3
    8 x=3
    Factor the numerator, what do you get?
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  8. #8
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    Re: Need some Calc 1 Help PLEASE!

    Quote Originally Posted by Bespetna View Post
    Final is tomorrow brahs....I NEED an A.

    I just Don't understand the steps to solving these, please show step by step what you do.







    For this last one I get 5sin^4 (x^3 +3)+sin^5 (3x^2)

    But he says the right answer is: 5sin^4 (x^3)cos(x^3 +3)(3x^2)

    Where do you get that cos?

    2) \lim_{x\to2^-}f(x)=\lim_{x\to2^+}f(x)=f(2)

    3) Answer to this question: Is \lim_{x\to 3^-}f(x)=\lim_{x\to 3^+}f(x)=f(3)?

    If the answer is not. Replace the 8 with other number. (Which?)

    1) f(x)=\sin^5(x^3+3)

    f'(x)=5\sin^4(x^3+3)\cos(x^3+3)\cdot 3x^2=15x^2\sin^4(x^3+3)\cos(x^3+3)
    Last edited by Ackbeet; July 25th 2011 at 06:00 PM.
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