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Continuity and Discontinuity

AP Calculus AB· difficulty 3/5

Let f(x)={x+3x<1kx2x≥1f(x) = \begin{cases} x + 3 & x < 1 \\ k x^2 & x \ge 1 \end{cases}. For what value of kk is ff continuous at x=1x = 1?

  • A

    22

  • B

    33

  • C

    11

  • D

    44

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Explanation

Need lim⁡x→1−f=lim⁡x→1+f\lim_{x\to 1^-} f = \lim_{x\to 1^+} f: 1+3=k(1)2⇒k=41 + 3 = k(1)^2 \Rightarrow k = 4.

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