# Continuity With Piece Wise Functions

1. Oct 6, 2015

### Michele Nunes

1. The problem statement, all variables and given/known data
Determine all values of the constant a such that the following function is continuous for all real numbers.
f(x) = ax/tan(x), x ≥ 0
= a2 - 2, x < 0
2. Relevant equations

3. The attempt at a solution
I tried so many different ways to get the first part of the function to be defined at 0 but nothing worked, I tried manipulating it with a bunch of trig identities and no matter what, that first part is always undefined at 0 so I don't know how the function can ever be continuous if that first part of the function is always going to be undefined at 0 and I can't remove it.

2. Oct 6, 2015

### Staff: Mentor

$$\lim_{x \to 0} \frac {\sin x} x = 1$$
Note that $\frac{ax}{\tan(x)} = a \frac x {\frac{\sin(x)}{\cos(x)}}$