Explanation If the limit of f ( x ) as x approaches to c is equal to the functional value of f ( x ) at c , then by definition of continuity of f we can say tha...

11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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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 14.3, Problem 9AYU

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To fill: If $\lim_{x \to c} f (x) = f (c)$ , then $f$ is __________ at _.

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Chapter 14.3, Problem 8AYU

Chapter 14.3, Problem 10AYU

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solve the following limit calculus problem

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As explained in Example 1.2.3 (right below the definition of limit), why does the function not have a limit as X 9 1 By the way, when the function doesn't have a limit, we can say the limit Does Not Exist and we can write it this way: lim g(x) DNE x-1 Because you only need to let x approach 1 from one side Because there is a hole in the graph When x approaches 1 from the left, g approaches a different value than when x approaches 1 from the right. So since g does NOT approach a single value as x approaches 1 from both sides, the limit doesn't exist. Because the graph of g is made up of different functions

Chapter 14 Solutions

Precalculus

Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1 Ch. 14.1 - Prob. 10AYU

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If lim x → c f ( x ) = f ( c ) , then f is ______________ at _____.