The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.)

Question

(a)    lim x→2 [f(x) + g(x)]

(b) lim x→ -1 f(x) / g(x)

(c)    lim x→1 3+f(x)

Answer 1

lim x→2 means what is the value of y as x approaches 2 from the left side and the right side - they must be the same value for the limit to exist. "Approaches" is the operative word - it does not have to exist at that y-value, as in example a. (Use it in a sentence: if you are approaching someone, then you are walking towards them and getting close but do not become that person.)

* lim x→1 [g(x)] = DNE because (left side of 1) lim x→1^- [g(x)] = 2 and (right side of 1) lim x→1⁺ [g(x)] = 1

(a)    lim x→2 [f(x) + g(x)] = 2 + 0 = 2