Explanation Given information : The function f ( x ) = x 3 − 9 x 2 − 39 x − 86 x − 13 that have to find its limiting value at a given point x = 13 . Calculation : On simplifying the given function using long division method, it is obtained: x − 13 ) x 3 − 9 x 2 − 39 x − 86 ( x 2 + 4 x + 13 x 3 − 13 x 2 ← 4 x 2 − 39 x on subtracting 4 x 2 − 39 x ← 13 x − 86 on subtracting 13 x − 169 ⇁ 83 on subtracting Thus, given function can be written as: x 3 − 9 x 2 − 39 x − 86 x − 13 = x 2 + 4 x + 13 + 83 x − 13 And accordingly, L i m x → 13 x 3 − 9 x 2 − 39 x − 86 x − 13 = L i m x → 13 ( x 2 + 4 x + 13 ) + L i m x → 13 ( 83 x − 13 ) = ( 13 2 + 4 ( 13 ) + 13 ) + L i m x → 13 ( 83 x − 13 )

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 2.1, Problem 52PS

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To estimate: Limx→13x3−9x2−39x−86x−13 by plotting the table for x and y values:

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Chapter 2.1, Problem 51PS

Chapter 2.1, Problem 53PS

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Chapter 2 Solutions

Student's Solution and Survival Manual for Calculus

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To estimate: L i m x → 13 x 3 − 9 x 2 − 39 x − 86 x − 13 by plotting the table for x and y values:

Solution Summary: The author calculates the limiting value of Limx13x39x239x-86 by simplifying the given function using long division method.

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To estimate: Limx→13x3−9x2−39x−86x−13 by plotting the table for x and y values:

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Chapter 2 Solutions