For the function shown below, find each of the following limits. (If an answer does not exist, enter DNE.)

Question

f(x) = 7x, x ≤ 0

x² + 9, x > 0^'

(a) lim f(x) = _____

x→0⁻

(b) lim f(x) = _____

x→0⁺

(c) lim f(x) = _____

x→0

Answer 1

(a) Limit will be 0

(b) Limit will be 9 (substitute x=0 into x² + 9). Note that the point (0,9) is not on the function but that isn't an issue as the limit does not have to be attained [ we just have to be able to get arbitrarily close]

(c) doesnt exist. If it did the left hand and right hand limits have to exist (which they do) and have to be equal (which they are not)