Explanation Given: lim x → 1 x 3 − 1 x 2 − 1 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 Constant rule: lim x → c k = k for any constant k Sum rule : lim x → c ( f ( x ) + g ( x ) ) = lim x → c f ( x ) + lim x → c g ( x ) Product rule: lim x → c [ f ( x ) g ( x ) ] = ( lim x → c f ( x ) ) ( lim x → c g ( x ) ) 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 f ( x ) for all values of x except at the troublesome value x = c Calculation: In order to evaluate the limit lim x → 1 x 3 − 1 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 29SP

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To evaluate the limit limx→1x3−1x2−1 .

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Chapter 2, Problem 28SP

Chapter 2, Problem 30SP

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43–46. Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 15.52) the directions of maximum increase, maximum decrease, and no change for f. ■ 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)

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Chapter 2 Solutions

Calculus

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To evaluate the limit lim x → 1 x 3 − 1 x 2 − 1 .

Solution Summary: The author explains the basic properties and rules for evaluating the limit undersetxto 1mathrmlim

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To evaluate the limit limx→1x3−1x2−1 .

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Chapter 2 Solutions