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

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2 years ago

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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)

Mathematics

1 answer:

ANEK [815] · Answer 1 · 2022-07-07T10:59:22+03:00

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