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If possible, choose k so that the following function is continuous on any interval:f(x)= (5x^4-20x^3...
4 months ago
Q:
If possible, choose k so that the following function is continuous on any interval:f(x)= (5x^4-20x^3)/(x-4) , x≠4f(x)= K , x=4k=?,
Accepted Solution
A:
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.