Answered: Question 5 Because the form 0 00 is…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question 5 parts a through d

* 00
818 818 818 8
LL
tells us very little about lim
(1)6
(a) Find formulas for f and g such that lim
is an
form that has a limit of o.
(1)f
is an
(b) Find formulas for f and g such that lim
form that has a limit of 0.
(1)6
(1)f
is an
6.
(c) Find formulas for f and g such that lim
form that has a limit of 1.
(1)f
is an
(I)6 00
(d) Find formulas for f and g such that lim
form that has a limit of 13.72.
Hint: you can answer each part by choosing f and g to be appropriate polynomials.
Question 5 Because the form 0 0o is indeterminate, knowing that functions f and g satisfy
lim f(x) = 0,
0 =
(T)6
tells us very little about lim f(r)g(x).
(a) Find formulas for f and g such that lim f(r)g(x) is a 0 0o form that has a limit of oo.
(b) Find formulas for f and g such that lim f(r)g(r) is a 0 0o form that has a limit of 0.
(c) Find formulas for f andg such that lim f(x)g(x) is a 0 0o form that has a limit of 1.
(d) Find formulas for f and g such that lim f(r)g(x) is a 0 0o form that has a limit of 13.72.
Hint: you cam answer each part by choosing f(x) and g(x) to each be of the form Cr" for appro-
priate constants C and
p.
Co-a
F10
F8
%23
%

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Follow-up Question

Because the form 0 ·∞ is indeterminate, knowing that functions f and g satisfy
limx→∞f (x) = 0, limx→∞g(x) = ∞
tells us very little about limx→∞f (x)g(x).
(a) Find formulas for f and g such that limx→∞f (x)g(x) is a 0 ·∞ form that has a limit of ∞.
(b) Find formulas for f and g such that limx→∞f (x)g(x) is a 0 ·∞ form that has a limit of 0.
(c) Find formulas for f and g such that limx→∞f (x)g(x) is a 0 ·∞ form that has a limit of 1.
(d) Find formulas for f and g such that limx→∞f (x)g(x) is a 0 ·∞ form that has a limit of 13.72.
Hint: you can answer each part by choosing f (x) and g(x) to each be of the form Cxp for appro-
priate constants C and p.

I only want the answer to question D.