Question

Given that lim x→a f(x) = 0 lim x→a g(x) = 0 lim x→a h(x) = 1 lim x→a p(x) = [infinity] lim x→a q(x) = [infinity], evaluate the limits below where possible. (If a limit is indeterminate, enter INDETERMINATE.) (a) lim x→a f(x) g(x) (b) lim x→a f(x) p(x) (c) lim x→a h(x) p(x) (d) lim x→a p(x) q(x)

Answer 1

Answer:

Step-by-step explanation:

We have to remind one of the properties of the limits:

Lim x→a  f(x)*g(x) = [Lim x→a f(x)]*[Lim x→a g(x)]

Hence, we evaluate the products of the limits

(a) Lim x→a  f(x)*g(x) = 0*0 = 0

(b) Lim x→a  f(x)*p(x) = 0*[infinity] = INDETERMINATE

(c) Lim x→a  h(x)*p(x) = 1*[infinity] = infinity

(d) Lim x→a  p(x)*q(x) = [infinity]*[infinity] = INDETERMINATE