- #1

999iscool

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## Homework Statement

Another similar question. I will appreciate any input!

[tex]\[f(x) = \left\{\begin{matrix}

x^{2}+a^{2} & x \leq 2\\ 2x+3a

& x > 2

\end{matrix}\right.\][/tex]

find a such f is continuous at x = 2

## Homework Equations

Well... the definition of continuity

## The Attempt at a Solution

So I have the first condition limit as x approaches 2 gives 4 + a^2

The second limit should equal to the first limit to agree (both left and right) and that limit gives 4+3a.

Equate the two, I solve for a

4 + 3a = 4+a^2

3a = a^2

a = 3

Am I right?

Thank you !

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