Finding the removable discontinuity

[999iscool]

Homework Statement

use the definition of continuity to find the values of a and c for which the function F is continuous at x = 1

$$\[f(x) = \left\{\begin{matrix}<br /> 2x-1 & x < 1\\ a+c<br /> & x = 1 \\ 3ax^2<br /> & x > 1<br /> \end{matrix}\right.\]$$

Homework Equations

The Attempt at a Solution

I know the definitions of continuity.
So I started it off with taking the limit of 2x - 1 as x approaches 1. I get 1.
Then I hit a problem.
Should I take the second limit for 3ax^2? If I do, I will get 3a.

According to the definition, I would need the limit equal to f(a). Which means limit of 2x-1 = f(a) , and this they must also equal to limit of 3ax^2.
If so I would hav3
1 (from the first limit) = 3a (from second limit) = a + c (that's where x = 1 is defined)
If so, I would have a = 1/3 and c = 2/3

Am I correct?

 

[Dick]

That's right.