a. Explanation Given: The given limit is lim x → 0 x 2 e − x . 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 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 b. To determine To evaluate the given limit

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 2.4, Problem 31PS

To determine

To evaluate the given limit limx→0x2e−x .

To determine

To evaluate the given limit

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Chapter 2.4, Problem 30PS

Chapter 2.4, Problem 32PS

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Chapter 2 Solutions

Calculus

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To evaluate the given limit lim x → 0 x 2 e − x .

Solution Summary: The author explains the basic properties and rules for limits of a polynomial function.