(a) Find formulas for f and g such that (b) Find formulas for f and g such that f(x) lim x→∞ g(x) f(x) lim x→∞ g(x) f(x) x→∞ g(x) (c) Find formulas for f and g such that lim is an is an is an 818 818 818 form that has a limit of ∞. form that has a limit of 0. form that has a limit of 1.
(a) Find formulas for f and g such that (b) Find formulas for f and g such that f(x) lim x→∞ g(x) f(x) lim x→∞ g(x) f(x) x→∞ g(x) (c) Find formulas for f and g such that lim is an is an is an 818 818 818 form that has a limit of ∞. form that has a limit of 0. form that has a limit of 1.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:Because the form
is indeterminate, knowing that functions f and g satisfy
lim f(x) = lim g(x) = = ∞
x →∞
x →∞
f(x)
tells us very little about lim
x→∞ g(x)
(a) Find formulas for f and g such that
(b) Find formulas for f and g such that
(c) Find formulas for f and g such that
lim
x →∞
(d) Find formulas for f and g such that
lim
x →∞
f(x)
g(x)
f(x)
g(x)
f(x)
lim
x→∞ g(x)
lim
x →∞
is an
is an
is an
88 88 88 88
is an
form that has a limit of ∞.
f(x)
g(x)
Hint: you can answer each part by choosing f and g to be appropriate polynomials.
form that has a limit of 0.
form that has a limit of 1.
form that has a limit of 13.72.
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