1. ## Removable Discontinuity problem.

Find the values of x(if any) at which f is not continuous and determine whether each such value is a removable discontinuity.

1. f(x) = x^2-4/x^3-8
2. f(x) = {2x-3, x is less than or equal to 2
x^2, x>2
3. f(x) = { 3x^2+5, x is not equal to 1
6, x=1

i dont really know where to start.i have read the book but can't really understand. someone help please.

2. First, please fix your notation. For #1, you have written $x^{2} - \frac{4}{x^{3}}-8$. I'm guessing this is not your intent.

A) Standard dogmat. Denominator = 0 spells discontinuity.
B) Help is on the way...If the numerator is also zero, for the same value of x, what can we do?

Thus, factor. Find common factors.

3. I guess ejaykasai meant $\frac{x^2-4}{x^3-8}$ Factorizing both numerator and denominator, you will get a factor $x-2$ in both cases. So the function is continuous at every point except at $x=2$.