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? asked in Science & MathematicsMathematics · 4 years ago

Calculus Piecewise Continuity Problem?

Find the value of K that will make the function continuous at all x

h(x) = (x^2 - k^2) / (x-k) , x is not equal to k

h(x) = 9 , x IS equal to k

I have already factored the top equation to (x-k)(x+k)/(x-k), so x-k cancels out which means there is a hole at k... Just confused on how to incorporate the bottom equation to fill the hole.

1 Answer

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  • husoski
    Lv 7
    4 years ago

    Simplify the first expression:

    h(x) = [(x + k)(x - k)] / (x - k) = (x + k) .... for all x != k.

    That has a lim x-->k h(x) = 2k.

    Since you need h(k) = lim x-->k h(x) for continuity, that means:

    9 = 2k

    k = 9/2

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