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;

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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