Explanation Consider the limit, lim x → 3 x 3 + c x 2 + 5 x + 12 x 2 − 7 x + 12 ….. (1) Here, as x tends to 3, the denominator also tends to zero, thus for the limit of the function to exist the numerator should also tend to zeroas x tends to 3. That is, 27 + 9 c + 15 + 12 = 0 9 c + 54 = 0 c = − 54 9 c = − 6 Substitute c = − 6 in equation (1), lim x → 3 x 3 − 6 x 2 + 5 x + 12 x 2 − 7 x + 12 = lim x → 3 ( x − 3 ) ( x 2

7th Edition

ISBN: 9781524916817

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

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, Problem 73SP

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To find: numberc so that limx→3x3+cx2+5x+12x2−7x+12 exists. Then find the corresponding limit.

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Chapter 2, Problem 72SP

Chapter 2, Problem 74SP

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Chapter 2 Solutions

Calculus

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numberc so that lim x → 3 x 3 + c x 2 + 5 x + 12 x 2 − 7 x + 12 exists. Then find the corresponding limit.

Solution Summary: The author explains that if undersetxto 3mathrmlim

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To find: numberc so that limx→3x3+cx2+5x+12x2−7x+12 exists. Then find the corresponding limit.

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Chapter 2 Solutions