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? asked in Science & MathematicsMathematics · 3 years ago

Help with Pre-Calc.?

Anna was asked to evaluate the limit as x approaches 4 of (x^2 - 16)/(x – 4).

She responded the limit was DNE. Is she right? Justify your answer.

3 Answers

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  • ?
    Lv 7
    3 years ago

    Anna is wrong

    f(x) = (x+4)(x-4)/(x-4) = x+4 for x ≠ 4

    lim x→4 = 8

  • ?
    Lv 7
    3 years ago

    lim (x²-16)/(x-4) =

    x→4

    ........(x+4)(x-4)

    lim ---------------- =

    x→4....(x-4)

    .....// Cancel out the (x-4) terms

    .....// from the numerator and

    .....// denominator to get

    lim (x+4) =

    x→4

    4+4 =

    8............ANS

  • hayharbr
    Lv 7
    3 years ago

    x^2 - 16 = (x - 4)(x + 4). As long as x never exactly equals 4 (which would make the bottom = 0), you can cancel the (x - 4) from top and bottom just leaving x + 4. So the limit as x approaches 4 is 8.

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