Explanation Given: A function: f ( x ) = x + 4 x − 8 Calculation: We know that a rational function is discontinuous, when the denominator is equal to zero. Let us find zeros of denominator as shown below: x − 8 = 0 x − 8 + 8 = 0 +

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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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 60SP

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Whether the given function is continuous on the interval [−5,5] . If not define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

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Chapter 2, Problem 59SP

Chapter 2, Problem 61SP

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Evaluate the following integrals, showing all your working

Consider the function f(x) = 2x³-4x2-x+1. (a) Without doing a sketch, show that the cubic equation has at least one solution on the interval [0,1]. Use a theorem discussed in lectures, or see Section 1.8 of Calculus (7th ed) by Stewart. Ensure that the conditions of the theorem are satisfied (include this in your solution) (b) Now, by sketching the cubic (by hand or by computer), you should see that there is, in fact, exactly one zero in the interval [0,1]. Use Newton's method to find this zero accurate to 3 decimal places. You should include a sketch of the cubic, Newton's iteration formula, and the list of iterates. [Use a computer if possible, e.g., a spreadsheet or MatLab.]

Evaluate the following integrals, showing all your working

Chapter 2 Solutions

Calculus

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Whether the given function is continuous on the interval [ − 5 , 5 ] . If not define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

Solution Summary: The author explains that a rational function is discontinuous when the denominator is equal to zero. Since 8 lies outside of the interval [-5,5], the given is continuous.

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Whether the given function is continuous on the interval [−5,5] . If not define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

Want to see the full answer?

Chapter 2 Solutions