Continuity and Discontinuity

AP Calculus AB· difficulty 3/5

Let f(x)={x24x2x2kx=2f(x) = \begin{cases} \dfrac{x^2 - 4}{x - 2} & x \ne 2 \\ k & x = 2 \end{cases}. Find kk so that ff is continuous at x=2x = 2.

  • A

    22

  • B

    00

  • C

    Cannot be made continuous

  • D

    44

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Explanation

For x2x \ne 2, the function reduces to x+2x + 2, with limit 44 as x2x \to 2. So set k=4k = 4.

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