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Math Help - Calculus Test Fixes

  1. #1
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    Calculus Test Fixes

    6.b. Consider the curve defined by the equation: y+\cos y=x+1 for 0<y<2\pi
    Write an equation for each vertical tangent to the curve. (Hint: Vertical lines are x=#)

    -I already found that y'=\frac{1}{1-\sin y}, but im not sure how to solve this one. how am i supposed to start off


    10. The expression \frac{1}{4}(\sqrt{1}+2\sqrt{\frac{5}{4}}+2\sqrt{2}  +2\sqrt{\frac{13}{4}}+\sqrt{5}) is the trapezoid approximation for which of the following definite integrals?

    This kind of expression always baffles me, it would really help if someone would care to explain


    2.a. Given that f is the function defined by f(x)=\frac{x^3-x}{x^3-4x}
    Find limit goes to infinity of f(x)

    -limits have always confused me. what am i supposed to be finding?

    2.b. Write an equation for each vertical and each horizontal asymptote to the graph of f.

    -i found that the vertical asymptotes are at x=0, x=2, x=-2 and horizontal at y=1, at least thats what i think. what am i supposed to with these?


    I appreciate all your help in advance.
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  2. #2
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    Quote Originally Posted by DarkestEvil View Post
    6.b. Consider the curve defined by the equation: y+\cos y=x+1 for 0<y<2\pi
    Write an equation for each vertical tangent to the curve. (Hint: Vertical lines are x=#)

    -I already found that y'=\frac{1}{1-\sin y}, but im not sure how to solve this one. how am i supposed to start off

    vertical tangent lines occur where the derivative is undefined ...
    1 - sin y = 0 ... solve for y



    10. The expression \frac{1}{4}(\sqrt{1}+2\sqrt{\frac{5}{4}}+2\sqrt{2}  +2\sqrt{\frac{13}{4}}+\sqrt{5}) is the trapezoid approximation for which of the following definite integrals?

    This kind of expression always baffles me, it would really help if someone would care to explain

    it might help to see the "integrals"


    2.a. Given that f is the function defined by f(x)=\frac{x^3-x}{x^3-4x}
    Find limit goes to infinity of f(x)

    -limits have always confused me. what am i supposed to be finding?

    the horizontal asymptote ... divide every term by the highest power of x and then take the limit as x goes to infinity

    2.b. Write an equation for each vertical and each horizontal asymptote to the graph of f.

    -i found that the vertical asymptotes are at x=0, x=2, x=-2 and horizontal at y=1, at least thats what i think. what am i supposed to with these?

    this part is correct except x = 0 is not a vertical asymptote ... it is a removable discontinuity (a hole)

    ...
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  3. #3
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    6.b. Oh I see, so in order for it to be undefined, y must equal \frac{\pi}{2}!

    10. I'm sorry the answer choices are:
    a. \int_{1}^{5}\sqrt{x} dx
    b. \int_{0}^{4}\sqrt{x^2+1} dx
    c. \int_{0}^{2}\sqrt{x^2+1} dx
    d. \int_{-1}^{2}\sqrt{x^2+1} dx
    e. \int_{1}^{3}\sqrt{x} dx

    2.a. Oh so since the x with the highest power on the top and bottom are x^3, \frac{x^3}{x^3}=1!

    2.b. I see your logic, so how am I supposed to write an equation for each of these values?
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  4. #4
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    Quote Originally Posted by DarkestEvil View Post
    6.b. Oh I see, so in order for it to be undefined, y must equal \frac{\pi}{2}!

    10. I'm sorry the answer choices are:
    a. \int_{1}^{5}\sqrt{x} dx
    b. \int_{0}^{4}\sqrt{x^2+1} dx
    c. \int_{0}^{2}\sqrt{x^2+1} dx
    d. \int_{-1}^{2}\sqrt{x^2+1} dx
    e. \int_{1}^{3}\sqrt{x} dx

    2.a. Oh so since the x with the highest power on the top and bottom are x^3, \frac{x^3}{x^3}=1!

    2.b. I see your logic, so how am I supposed to write an equation for each of these values?

    Actually, y = \frac{\pi}{2} + 2\pi n where n is an integer representing how many times you have gone around the unit circle.
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  5. #5
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    Quote Originally Posted by Prove It View Post
    Actually, y = \frac{\pi}{2} + 2\pi n where n is an integer representing how many times you have gone around the unit circle.
    well played, thanks
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  6. #6
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    Quote Originally Posted by Prove It View Post
    Actually, y = \frac{\pi}{2} + 2\pi n where n is an integer representing how many times you have gone around the unit circle.
    the problem statement says 0 < y < 2\pi
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  7. #7
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    Quote Originally Posted by skeeter View Post
    the problem statement says 0 < y < 2\pi
    Ah, true.

    I was just giving our OP a valuable lesson in "reading the question properly"
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