Amenah8
  • Amenah8
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Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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Amenah8
  • Amenah8
\[\lim_{x \rightarrow \pm \infty} (x^4+x^3)/(12x^3+128)\]
freckles
  • freckles
divide top and bottom by x^3
freckles
  • freckles
we are dividing top and bottom by x^3 because the degree of the bottom polynomial is 3

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freckles
  • freckles
\[\lim_{x \rightarrow \infty} \frac{\frac{x^4}{x^3}+\frac{x^3}{x^3}}{\frac{12x^3}{x^3}+\frac{128}{x^3}}\]
freckles
  • freckles
now figure out the limit for each of those mini-fractions
Amenah8
  • Amenah8
oh!i remember how to do this! one moment while i work it out, please?
Amenah8
  • Amenah8
\[(x+1)/(12+128/x^3)\]
Amenah8
  • Amenah8
and then replace x with 0, right?
Amenah8
  • Amenah8
i mean with infinity
freckles
  • freckles
right now you must look at x approaches infinity and also x approaches -negative infinity
Amenah8
  • Amenah8
\[\infty+1/12+0\] ?
freckles
  • freckles
so you have infinity for x approaches infinity ok now you need to evaluate your second question which involves x going to -infinity
Amenah8
  • Amenah8
ok, one moment
Amenah8
  • Amenah8
\[-\infty+1/12+0\] ?
freckles
  • freckles
right so you have: \[\lim_{x \rightarrow \infty}\frac{x+1}{12+\frac{128}{x^3}} =\frac{\infty}{12+0}=\infty \\ \lim_{x \rightarrow -\infty} \frac{x+1}{12+\frac{128}{x^3}}=\frac{-\infty}{12+0}=-\infty\]
freckles
  • freckles
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
Amenah8
  • Amenah8
haha, okay! thank you so much!
freckles
  • freckles
np

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