I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.

I need to find:

the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)

and the lim as x goes to zero of the same function

Please help!

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- Aug 31st 2006, 05:33 AMafn2Urgent Help! with Limits
I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.

I need to find:

the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)

and the lim as x goes to zero of the same function

Please help! - Aug 31st 2006, 06:10 AMgalactus
When taking the limit of a rational expression, if x approaches +/- infinity, you can disregard all but the coefficients of the highest powers.

Therefore you have,

$\displaystyle \lim_{x\to\infty}\frac{3x^{2}}{4x^{2}}$

Now, you can see what it is?.

As x approaches 0, look close, can you see it?. - Aug 31st 2006, 06:39 AMThePerfectHackerQuote:

Originally Posted by**afn2**

$\displaystyle \lim_{x\to\infty}\frac{3+\frac{2}{x}+\frac{2}{x^2} }{4+\frac{2}{x}+\frac{7}{x^2}}$

The numerator is,

$\displaystyle \lim_{x\to\infty} 3+\frac{2}{x}+\frac{2}{x^2}=3$

The denominaot is,

$\displaystyle \lim_{x\to\infty}4+\frac{2}{x}+\frac{7}{x^2}=4$

Since both limits exists thus the value of the limit is 3/4 - Aug 31st 2006, 06:57 AMtopsquarkQuote:

Originally Posted by**afn2**

-Dan - Aug 31st 2006, 07:50 AMafn2
Thanks a bunch, I knew it was pretty simple, but I've always struggled with limits, even though I completely get derivatives and integrals. I just needed a push in the right direction. Thanks guys!