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Amenah8

  • one year ago

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  1. Amenah8
    • one year ago
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    \[\lim_{x \rightarrow \pm \infty} (x^4+x^3)/(12x^3+128)\]

  2. freckles
    • one year ago
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    divide top and bottom by x^3

  3. freckles
    • one year ago
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    we are dividing top and bottom by x^3 because the degree of the bottom polynomial is 3

  4. freckles
    • one year ago
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    \[\lim_{x \rightarrow \infty} \frac{\frac{x^4}{x^3}+\frac{x^3}{x^3}}{\frac{12x^3}{x^3}+\frac{128}{x^3}}\]

  5. freckles
    • one year ago
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    now figure out the limit for each of those mini-fractions

  6. Amenah8
    • one year ago
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    oh!i remember how to do this! one moment while i work it out, please?

  7. Amenah8
    • one year ago
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    \[(x+1)/(12+128/x^3)\]

  8. Amenah8
    • one year ago
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    and then replace x with 0, right?

  9. Amenah8
    • one year ago
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    i mean with infinity

  10. freckles
    • one year ago
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    right now you must look at x approaches infinity and also x approaches -negative infinity

  11. Amenah8
    • one year ago
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    \[\infty+1/12+0\] ?

  12. freckles
    • one year ago
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    so you have infinity for x approaches infinity ok now you need to evaluate your second question which involves x going to -infinity

  13. Amenah8
    • one year ago
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    ok, one moment

  14. Amenah8
    • one year ago
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    \[-\infty+1/12+0\] ?

  15. freckles
    • one year ago
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    right so you have: \[\lim_{x \rightarrow \infty}\frac{x+1}{12+\frac{128}{x^3}} =\frac{\infty}{12+0}=\infty \\ \lim_{x \rightarrow -\infty} \frac{x+1}{12+\frac{128}{x^3}}=\frac{-\infty}{12+0}=-\infty\]

  16. freckles
    • one year ago
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    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

  17. Amenah8
    • one year ago
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    haha, okay! thank you so much!

  18. freckles
    • one year ago
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    np

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