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Math Help - limits quest

  1. #1
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    limits quest

    lim x^4-1 / x-1
    x-1

    the answer is 4 but i donno how so if anyone could tell me i'd appreciate it.
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  2. #2
    Super Member PaulRS's Avatar
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    What you need is a good factorization

    x^4-1=(x^2-1)\cdot{(x^2+1)}=(x-1)\cdot{(x+1)}\cdot{(x^2+1)}

    Then \lim_{x\rightarrow{1}}{\frac{x^4-1}{x-1}}=\lim_{x\rightarrow{1}}{\frac{(x-1)\cdot{(x+1)}\cdot{(x^2+1)}}{x-1}}=\lim_{x\rightarrow{1}}{(x+1)\cdot{(x^2+1)}}=4
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  3. #3
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    thx aloooot
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