Explanation Given: The given limit is lim x → π 2 cos 2 x cos x 2 . Concept Used: Basic properties and rules for limits: for any real number c, suppose that functions f and g has limit at x = c , then 1. Constant rule: lim x → c k = k for any constant k 2. Sum rule : lim x → c ( f ( x ) + g ( x ) ) = lim x → c f ( x ) + lim x → c g ( x ) 3. Product rule: lim x → c [ f ( x ) g ( x ) ] = ( lim x → c f ( x ) ) ( lim x → c g ( x ) ) 4. Quotient rule : lim x → c [ f ( x ) g ( x ) ] = lim x → c f ( x ) lim x → c g ( x ) if lim x → c g ( x ) ≠ 0 Limit of a polynomial function is defined as: lim x → c P ( x ) = P ( c ) If the limit if a function f ( x ) cannot be evaluated when x → c by direct substitution, try to reduce the function to another function that agrees with

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 5, Problem 8CRP

To determine

To evaluate: the given limit limx→π2cos2xcosx2 .

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Chapter 5, Problem 7CRP

Chapter 5, Problem 9CRP

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Chapter 5 Solutions

Calculus

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the given limit lim x → π 2 cos 2 x cos x 2 .

Solution Summary: The author explains the basic properties and rules for limits: for any real number c, suppose that functions f and g have limit at x=c

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To evaluate: the given limit limx→π2cos2xcosx2 .

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Chapter 5 Solutions