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)

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

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

step-by-step explanation: