Question 4 Because the form is indeterminate, knowing that functions f and g satisfy lim f(x) lim g(x) = ∞ f(x) tells us very little about lim x→0 g(x) (a) Find formulas for f and g such that lim f(x) is an form that has a limit of o. x→00 g(x) f(x) 2+0 g(x) (b) Find formulas for f and g such that lim is an form that has a limit of 0. f(x) x→0 g(x) (c) Find formulas for f and g such that lim is an form that has a limit of 1. (d) Find formulas for f and g such that lim f(x) is an form that has a limit of 13.72. x→0 g(x) 00 Hint: you can answer each part by choosing ƒ and g to be appropriate polynomials. Question 5 Because the form 0 · ∞ is indeterminate, knowing that functions f and g satisfy lim f(x) = 0, lim g(x) = o∞ tells us very little about lim f(x)g(x). エ→0 (a) Find formulas for f and g such that lim f(x)g(x) is a 0 · ∞ form that has a limit of o. (b) Find formulas for f and g such that lim f(x)g(x) is a 0·∞ form that has a limit of 0. (c) Find formulas for f and g such that lim f(x)g(x) is a 0 · ∞ form that has a limit of 1. (d) Find formulas for f and g such that lim 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 Cx³ for ap priate constants C and p. 818 818 8|8 8|8

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