Math problem with limits?

lim x→−∞

3x^8 −2x^4 + 1 / −7x^12 −5x^3 + x

Answer is 0.What i do is differentiate it first.Factor the top part like 8x^3(3x^4-1).I make a reduction with the bottom part and removing all the top x.Then we have constans over infinity which is 0.Am i stupid ? Is that how you do it ?

1 Answer

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  • 4 months ago

    The term with the highest exponent dominates as you approach infinity.

    Numerator 3x^8

    Denominator -7x^12

    The denominator's exponent is larger, so this goes to 0.

    If the denominator's exponent were smaller, it would go to -infinity. Negative because of the sign.

    If the largest exponents were the same, it would go to a simple fraction of the leading coefficients. -3/7

    • Bory4 months agoReport

      Nevermind it just clicked in my brain,thank you.

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