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Question
Thank you for taking the time to answer my question. It is:

Determine the value of c so that the function below s continuous:

f(x)=
2x-5    x<2
cx^2    x(is equal to or greater than)2

Answer
That function is f(x) = { 2x - 5 for x < 2 / cx^2 for x>= 2 }.
To be continuous, the value at x=2 must be the same on both sides.

On the left it is 2x - 5 at x=2, and that is 2(2) - 5 = -1.

On the right, it is cx^2 for x=2, so it is 4c.

We need -1 = 4c, so solving gives us c = -1/4.

That way when we know the value is 4c, it is really -1, and that is the same.

Calculus

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