Explanation Given information: f & g are continuous at x = c & g ( x ) ≠ 0 . Proof: Sincef & g are continuous at x = c then f(c)&g(c) are exist. The lim x → c f ( x ) , lim x → c g ( x ) , are exist. lim x → c f ( x ) = f ( c ) & lim x → c g ( x ) = g ( c ) Since g ( x ) ≠ 0 then z ( x ) = f ( x ) g ( x ) ............ (i) it is defined everywhere, hence z ( c ) = f ( c ) g ( c ) Now taking limit x → c on both side in equation (i)

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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Question

Chapter 2.3, Problem 50PS

To determine

To prove: fg is continuous at x = c iff & g are continuous.

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Chapter 2.3, Problem 49PS

Chapter 2.3, Problem 51PS

Chapter 2 Solutions

Calculus

Ch. 2.1 - Prob. 1PS Ch. 2.1 - Prob. 2PS Ch. 2.1 - Prob. 3PS Ch. 2.1 - Prob. 4PS Ch. 2.1 - Prob. 5PS Ch. 2.1 - Prob. 6PS Ch. 2.1 - Prob. 7PS Ch. 2.1 - Prob. 8PS Ch. 2.1 - Prob. 9PS Ch. 2.1 - Prob. 10PS

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