By the end behavior of a function we mean the behavior of its values as x → ∞ and as x → –∞.
(a) Describe and compare the end behavior of the functions
P(x) = 3x5 – 5x3 + 2x Q(x) = 3x5
by graphing both functions in the viewing rectangles [– 2, 2] by [– 2, 2] and [– 10, 10] by [– 10,000, 10,000].
(b) Two functions are said to have the same end behavior if their ratio approaches 1 as x → ∞. Show that P and Q have the same end behavior.
Multivariable Calculus
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