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25 June, 05:34

If possible, choose k so that the following function is continuous on any interval:

f (x) = (5x^4-20x^3) / (x-4), x≠4

f (x) = K, x=4

k=?,

+4
Answers (1)
  1. 25 June, 07:57
    0
    We need to cancel out the discontinuity in x = 4

    In order to do that, factorize the numerator:

    5x⁴ - 20x³ = 5x³ (x-4)

    This way, your function will be:

    f (x) = 5x³ (x-4) / (x-4)

    and the two parentheses cancel out, leaving

    f (x) = 5x³

    which at x = 4 gives:

    f (4) = 5·4³ = 5 · 64 = 320

    Therefore K = 320.
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