Explanation Given information: f ( x ) = ⌊ x + 3 ⌋ + ⌊ 2 x ⌋ Calculation: Assume that f ( x ) is defined on an open interval containing x = c . Then f is continuous at x = c if: lim x → c f ( x ) = f ( c ) . If the limit does not exist, of if exists but is not equal to f ( c ) , then f has discontinuity (or is discontinuous) at x = c . A function is called: Left continuous at x = c if lim x → c − f ( x ) = f ( c ) Right continuous at x = c if lim x → c + f ( x ) = f ( c ) If the one-sided limit lim x → c − f ( x ) = f ( c ) and lim x → c + f ( x ) = f ( c ) exist but are not equal, then it is known as jump discontinuity. Given function is f ( x ) = cos ( π ⌊ x ⌋ ) . The graph of f ( x ) = cos ( π ⌊ x ⌋ ) is as follows:

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 2.4, Problem 37E

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To find:points of discontinuity (removable, jump, infinite or none of these) and whether the functions is left-or right-continuous.

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Chapter 2.4, Problem 36E

Chapter 2.4, Problem 38E

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For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y= f(x) = x²+x; x=-1,x=2 a. Which of the following formulas can be used to find the slope of the secant line? ○ A. 2-(-1) f(2) f(-1) 2+(-1) C. 1(2)+(-1) The equation of the secant line is 1(2)+(-1) О в. 2+(-1) f(2)-(-1) D. 2-(-1)

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Chapter 2 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.2 - Prob. 1PQ Ch. 2.2 - Prob. 2PQ Ch. 2.2 - Prob. 3PQ Ch. 2.2 - Prob. 4PQ Ch. 2.2 - Prob. 5PQ Ch. 2.2 - Prob. 6PQ Ch. 2.2 - Prob. 7PQ Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - 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points of discontinuity (removable, jump, infinite or none of these) and whether the functions is left-or right-continuous.

Solution Summary: The author explains that the function is left- or right-continuous. If the one-sided limit exists but is not equal to f(x), it is known as jump discontinuity.

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To find:points of discontinuity (removable, jump, infinite or none of these) and whether the functions is left-or right-continuous.

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Chapter 2 Solutions