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March 28, 2017

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For what values of a and b that make the function f continuous everywhere.

f(x)={(x^2-4)/(x-2) if x<2
ax^2-bx-18 if 2<x<3
10x-a+b if x>3

  • calculus - ,

    There are three segments of functions, and two possibly discontinuous points, at x=2 and x=3.

    Equate the adjacent segments to find the value of a and b that make the segments have the same values at x=2 and x=3.

    Finally, check that the limits approaching from each side (2- and 2+, 3- and 3+) of the combined function are identical. They should be if the function is continuous.

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