Find the following limits. (If an answer does not exist, enter DNE.)

Question

x² + 1 if x < 2

f(x) = {

(x − 3)² if x ≥ 2

1. lim x → 2⁻ f(x)=

2. lim x → 2⁺ f(x) =

Answer 1

Simon,

The first limit is from the left for values of x that are less than 2. What is f(x) equal to when x is less than 2? What is the limit of this expression as x approaches 2?

The second limit is from the right for values of x that are greater than 2. What is f(x) equal to when x is greater than 2? What is the limit of this expression as x approaches 2?