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Answer to Question #762 in Calculus for vic

Question #762
Determine the values of c∈R so as to make the following function continuous on R.

f(x)= {c(x^2) + 2x, x < 2
{x^3 - cx x ≥ 2
Expert's answer
If the function meets the continuity conditions at some point, it should exist in this point and its limits from both sides should be equal to each other.
lim_(x->2(-)) = C(2^2)+2*2 = 4C+4; x<2
lim (x->2(+)) = 2^3 - C*2 = 8-2C; x ≥ 2
4C+4 = 8-2C;
6C = -4;
C = -2/3;

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