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Determining Limits Using Algebraic Manipulation

AP Calculus AB· difficulty 2/5

Evaluate lim⁡x→5x2−25x2−6x+5\displaystyle\lim_{x\to 5}\dfrac{x^2 - 25}{x^2 - 6x + 5}.

  • A

    11

  • B

    Does not exist

  • C

    52\tfrac{5}{2}

    check_circle
  • D

    25\tfrac{2}{5}

Explanation

Top: (x−5)(x+5)(x-5)(x+5). Bottom: (x−5)(x−1)(x-5)(x-1). Cancel: (x+5)/(x−1)(x+5)/(x-1). At x=5x = 5: 10/4=5/210/4 = 5/2.

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