a. Explanation The given function is f ( x ) = 4 x 3 + x 2 + 7 x 2 − x + 1 . Divide both the numerator and denominator by the highest power of x in the denominator. f ( x ) = 4 x + x 2 x 2 + 7 x 2 1 − x x 2 + 1 x 2 f ( x ) = 4 x + 1 + 7 x 2 1 − 1 x + 1 x 2 (1) Take limit as x approaches positive infinity on both sides of the equation (1). lim x → ∞ f ( x ) = lim x → ∞ 4 x + 1 + 7 x 2 1 − 1 x + 1 x 2 = ( lim x → ∞ 4 x + lim x → ∞ 1 + lim x → ∞ 7 x 2 ) ( lim x → ∞ 1 − lim x → ∞ 1 x + lim x → ∞ 1 x 2 ) = ∞ Thus, the limit of the function is ∞ b. To determine Whether the function f ( x ) = 4 x 3 + x 2 + 7 x 2 − x + 1 has a slant asymptote. If exists to write the equation of the slant asymptote.

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

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ISBN: 9780135243435

Author: Bill Briggs

Publisher: Pearson Education (US)

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Chapter 2, Problem 65RE

To determine

The limits limx→∞f(x) and limx→−∞f(x), where f(x)=4x3+x2+7x2−x+1.

To determine

Whether the function f(x)=4x3+x2+7x2−x+1 has a slant asymptote. If exists to write the equation of the slant asymptote.

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Chapter 2, Problem 64RE

Chapter 2, Problem 66RE

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Ch. 2.1 - In Example 1, what is the average velocity between...Ch. 2.1 - Explain the difference between average velocity...Ch. 2.1 - Prob. 3QC Ch. 2.1 - Suppose s(t) is the position of an object moving...Ch. 2.1 - Suppose s(t) is the position of an object moving...Ch. 2.1 - Basic Skills 7. Average velocity The function s(t)...Ch. 2.1 - Average velocity The function s(t) represents the...Ch. 2.1 - Average velocity The table gives the position s(t)...Ch. 2.1 - Average velocity The graph gives the position s(t)...Ch. 2.1 - Instantaneous velocity The following table gives...

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The limits lim x → ∞ f ( x ) and lim x → − ∞ f ( x ) , where f ( x ) = 4 x 3 + x 2 + 7 x 2 − x + 1 .

Solution Summary: The author explains the limits of undersetxtoinftymathrmlimf(x-) and