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

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• May 17th 2008, 09:51 AM
Pikeman85
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.

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)
• May 17th 2008, 09:57 AM
galactus
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.
• May 17th 2008, 10:00 AM
Moo
Hello,

Quote:

Originally Posted by galactus
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 :

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

?
• May 17th 2008, 10:02 AM
Pikeman85
That would seem to give me -4.93, which doesn't work when I try to input the answer.
• May 17th 2008, 10:04 AM
Moo
Quote:

Originally Posted by Pikeman85
That would seem to give me -4.93, which doesn't work when I try to input the answer.

Because it's approximative ?
• May 17th 2008, 10:05 AM
Pikeman85
I put it into the math homework submitter thing, WebCT.

This time I tried -4.9375, and still got incorrect.
• May 17th 2008, 10:07 AM
Moo
Quote:

Originally Posted by Pikeman85
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
• May 17th 2008, 10:11 AM
Pikeman85
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 :)
• May 17th 2008, 10:17 AM
galactus
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
• May 17th 2008, 10:20 AM
galactus
Quote:

((6x + 10)/(x - 7)) * ((7x - 2)/(-x - 8))
Is this another limit as x--> -infinity?. If so, did you get -42?.
• May 17th 2008, 10:21 AM
Pikeman85
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.
• May 17th 2008, 10:22 AM
Pikeman85
Yes, I got -42 for that one. It was quite easy after the first one in that sequence, I was just daunted by it.
• May 17th 2008, 10:28 AM
Moo
Quote:

Originally Posted by Pikeman85
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}\\
&=\frac{(x^2+8x-10)-x^2}{\sqrt{x^2+8x-10}+x} \\
&=\frac{8x-10}{\sqrt{x^2+8x-10}+x} \\
&=\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..
• May 17th 2008, 10:35 AM
janvdl
I believe the help given here might be illegal. Let the moderators investigate. I know what the WebCT system is and how it works...
• May 17th 2008, 10:36 AM
Pikeman85
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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