Math Help? Calculus?

Question

if f(x) ={1-x^2 if 0 lessthen equal to x less than equal to 1
1+ x/2 if 1 Show that f is not continuous on [0,2].
Please Show steps!

Answer 1

The left-hand limit at 1 is lim (x -> 1-) (1 - x^2) = 0. The right-hand limit is lim (x -> 1+) (1 + x/2) = 3/2. Since the limits are different, the limit does not exist, so the function is not continuous at 1.

Answer 2

Graph both functions on the same set of axis over the correct domain. You will see that the graphs do not connect at x=1. Therefore there is no continuity.