Explanation Continuity theorem consists five different kinds of theorem, Theorem 1 All polynomial functions and also the functions sin x , cos x , tan − 1 x , e x are continuous on the interval ( − ∞ , ∞ ) . Theorem 2 A rational function is continuous everywhere except at the values of x that make the denominator of the function capable to zero. Theorem 3 If functions g and f are continuous at x = a , then a)At x = a , ( f - g ) is continuous. b)At x = a, ( f + g ) is continuous. c) ( f . g ) is continuous at x = a . d) (f/g) is continuous at x = a if g ( a ) is not capable to zero. Theorem 4 If g could be a continuous function at x = a and function f is also continuous at g ( a ), then the composition f o g is continuous at x = a

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 7PE

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The continuity theorem.

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Calculus

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