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Math Help - Need Calculus assistance with several problems! I have a date tonight!

  1. #1
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    Need Calculus assistance with several problems! I have a date tonight!

    I am very sorry with being so urgent, however I am having terrible trouble with my Calculus homework - can't figure it out at all and I am working for hours at it.

    I have several problems that I may need help explaining. I would prefer not to just get the answer, and so would prefer just hints for now, however I really want/need to get full credit on this assignment, and I have a date set for 7 PM tonight.

    Please help me

    The first problem I have issues with is:

    Find the limit of x approaches negative infinity of the function: ((10-15x)/(9+x)) + ((9x^2 + 13)/(12x-5)^2)
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  2. #2
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    You could rewrite as:

    \frac{-711x^{3}+2121x^{2}-1312x+367}{144x^{3}+1176x^{2}-1055x+225}

    Now, keep in mind that when finding the limit of a rational expression as x\rightarrow{\pm\infty}, you can ignore everything except the highest powers.
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  3. #3
    Moo
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    Hello,

    Quote Originally Posted by galactus View Post
    You could rewrite as:

    \frac{-711x^{3}+2121x^{2}-1312x+367}{144x^{3}+1176x^{2}-1055x+225}

    Now, keep in mind that when finding the limit of a rational expression as x\rightarrow{\pm\infty}, you can ignore everything except the highest powers.
    Wouldn't it be better to write this way :

    \frac{10-15x}{9+x}+\frac{9x^2 + 13}{(12x-5)^2}=\frac{10-15x}{9+x}+\frac{9x^2 + 13}{144x^2-120x+25}

    ?
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  4. #4
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    That would seem to give me -4.93, which doesn't work when I try to input the answer.
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  5. #5
    Moo
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    Quote Originally Posted by Pikeman85 View Post
    That would seem to give me -4.93, which doesn't work when I try to input the answer.
    Because it's approximative ?
    Where did you put your answer ?
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  6. #6
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    I put it into the math homework submitter thing, WebCT.

    This time I tried -4.9375, and still got incorrect.
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  7. #7
    Moo
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    Quote Originally Posted by Pikeman85 View Post
    I put it into the math homework submitter thing, WebCT.

    This time I tried -4.9375, and still got incorrect.
    Then try -15+9/144=-239/16

    It's better keeping the exact values
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  8. #8
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    Thank you! How did you get that?! What was I doing wrong? I thought I was using the values correctly. EDIT: I realized that I used a positive 15 and you a negative, would that be because it is approaching negative infinity? If so, that was such a stupid error on my part as I had gotten 15.06... earlier.

    And now time for the next question (there's a lot, so feel free to help only as much as you want to guys. I might start coming here frequently just so I can understand this stuff better)

    ((6x + 10)/(x - 7)) * ((7x - 2)/(-x - 8))

    I got this one, was relatively easy after figuring exactly how I went wrong on the last one
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  9. #9
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    I wrote it that way with a common denominator so we could see the coefficients of the highest powers are

    -711/144 = -79/16 = -4.9375
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  10. #10
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    ((6x + 10)/(x - 7)) * ((7x - 2)/(-x - 8))
    Is this another limit as x--> -infinity?. If so, did you get -42?.
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  11. #11
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    Now this next one has been giving me trouble.

    It is as the limit approaches positive infinity, of sqrt [x^2 + 8x - 10] - x

    I tried to figure this one out by multiplying it by sqrt [x^2 + 8x - 10] + x, but this did not seem to work out.
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  12. #12
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    Yes, I got -42 for that one. It was quite easy after the first one in that sequence, I was just daunted by it.
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  13. #13
    Moo
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    Quote Originally Posted by Pikeman85 View Post
    Now this next one has been giving me trouble.

    It is as the limit approaches positive infinity, of sqrt [x^2 + 8x - 10] - x

    I tried to figure this one out by multiplying it by sqrt [x^2 + 8x - 10] + x, but this did not seem to work out.
    \begin{aligned} \sqrt{x^2+8x-10}-x &=(\sqrt{x^2+8x-10}-x) \cdot \frac{\sqrt{x^2+8x-10}+x}{\sqrt{x^2+8x-10}+x}\\<br />
&=\frac{(x^2+8x-10)-x^2}{\sqrt{x^2+8x-10}+x} \\<br />
&=\frac{8x-10}{\sqrt{x^2+8x-10}+x} \\<br />
&=\frac{8-\frac{10}{x}}{\sqrt{1+\frac 8x-\frac{10}{x^2}}+1} \end{aligned}

    Above, it tends to 8, below, it tends to 2..
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  14. #14
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    I believe the help given here might be illegal. Let the moderators investigate. I know what the WebCT system is and how it works...
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  15. #15
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    Neither 8 nor 2 worked, and unbounded isn't an option.

    As I said, I tried to calculate it out with the equation I specified.
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