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\[\lim_{x \rightarrow \pm \infty} (x^4+x^3)/(12x^3+128)\]
divide top and bottom by x^3
we are dividing top and bottom by x^3 because the degree of the bottom polynomial is 3

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\[\lim_{x \rightarrow \infty} \frac{\frac{x^4}{x^3}+\frac{x^3}{x^3}}{\frac{12x^3}{x^3}+\frac{128}{x^3}}\]
now figure out the limit for each of those mini-fractions
oh!i remember how to do this! one moment while i work it out, please?
\[(x+1)/(12+128/x^3)\]
and then replace x with 0, right?
i mean with infinity
right now you must look at x approaches infinity and also x approaches -negative infinity
\[\infty+1/12+0\] ?
so you have infinity for x approaches infinity ok now you need to evaluate your second question which involves x going to -infinity
ok, one moment
\[-\infty+1/12+0\] ?
right so you have: \[\lim_{x \rightarrow \infty}\frac{x+1}{12+\frac{128}{x^3}} =\frac{\infty}{12+0}=\infty \\ \lim_{x \rightarrow -\infty} \frac{x+1}{12+\frac{128}{x^3}}=\frac{-\infty}{12+0}=-\infty\]
also I like to separate my numerators by doing ( ) and my denominators by doing ( ) like I would write what you said like (-infty+1)/(12+0) it is more proper and correct :p
haha, okay! thank you so much!
np

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