Finding Limits at Infinity In Exercises 11 and 12, find lim x → ∞ h ( x ) , if it exists. f ( x ) = 5 x 3 − 3 (a) h ( x ) = f ( x ) x 2 (b) h ( x ) = f ( x ) x 3 (c) h ( x ) = f ( x ) x 4
Finding Limits at Infinity In Exercises 11 and 12, find lim x → ∞ h ( x ) , if it exists. f ( x ) = 5 x 3 − 3 (a) h ( x ) = f ( x ) x 2 (b) h ( x ) = f ( x ) x 3 (c) h ( x ) = f ( x ) x 4
Solution Summary: The author explains how the limit of a rational function at infinity could be computed.
Sketch the graph of an example of a function f that satisfies all of the given conditions.
lim x→0 f(x) = 4, lim x→8− f(x) = 1, lim x→8+ f(x) = −2, f(0) = 5, f(8) = 0
Sketch the graph of an example of a function f that satisfies all of the given conditions.
lim f(x) = ∞,
lim f(x) =5,
lim f(x) = -5
6.
x→2
x→-2+
x→-2-
lim f(x) = 0,
lim f(x) = 0,
f(0) = 0
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