Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Concept explainers

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, Problem 26RE

(a)

To determine

To find: The value of limx→1−k(x) .

(a)

Expert Solution

Answer to Problem 26RE

The value of limx→1−k(x) is 1.5.

Explanation of Solution

Given information: The domain of the function is −1≤x≤3 . The graph is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2, Problem 26RE , additional homework tip 1

Calculation:

From the given graph, it can be observed that as x approaches 1 from left then the function approaches to 1.5.

limx→1−k(x)=1.5

Therefore, the value of limx→1−k(x) is 1.5.

(b)

To determine

To find: The value of limx→1+k(x) .

(b)

Expert Solution

Answer to Problem 26RE

The value of limx→1+k(x) is 0.

Explanation of Solution

Given information: The domain of the function is −1≤x≤3 . The graph is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2, Problem 26RE , additional homework tip 2

Calculation:

From the given graph, it can be observed that as x approaches 1 from right then the function approaches to 0.

limx→1+k(x)=0

Therefore, the value of limx→1+k(x) is 0.

(c)

To determine

To find: The value of k(1) .

(c)

Expert Solution

Answer to Problem 26RE

The value is k(1) is 0.

Explanation of Solution

Given information: The domain of the function is −1≤x≤3 . The graph is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2, Problem 26RE , additional homework tip 3

Calculation:

From the graph, it can be observed that the value of the function y=f(x) at x=1 is 0.

k(1)=0

Therefore, the value is k(1) is 0.

(d)

To determine

To find: Whether k(x) is continuous at x=1 or not.

(d)

Expert Solution

Answer to Problem 26RE

The function k(x) is discontinuous at x=1 .

Explanation of Solution

Given information: The domain of the function is −1≤x≤3 . The graph is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2, Problem 26RE , additional homework tip 4

Calculation:

From the graph, it can be observed that, at x=1 there is a jump on the graph of the function. The jump shows the discontinuity as the left hand limit is not equal to the right hand limit of the function.

limx→1−k(x)≠limx→1+k(x)

Therefore, the function is discontinuous at x=1 .

(e)

To determine

To find: The points of discontinuity of k(x) .

(e)

Expert Solution

Answer to Problem 26RE

The point of discontinuity of the given function is x=1 .

Explanation of Solution

Given information: The domain of the function is −1≤x≤3 . The graph is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2, Problem 26RE , additional homework tip 5

Calculation:

A function y=f(x) is said to be continuous if f(c)=limx→c+f(x)=limx→c−f(x) .

It is already known that at x=1 left hand limit is not equal to right hand limit of the function. So, function is discontinuous at x=1 .

Therefore, the point of discontinuity of the given function is x=1 .

(f)

To determine

To find: Whether any point of discontinuity can be removed, if so describe new function and if not explain.

(f)

Expert Solution

Answer to Problem 26RE

There is no point for removable discontinuity.

Explanation of Solution

Given information: The domain of the function is −1≤x≤3 . The graph is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2, Problem 26RE , additional homework tip 6

Calculation:

The discontinuity can be removable if left hand limit and right hand limit are equal. The right hand limit and left hand limit at x=1 are not equal.

The discontinuity is not removable because the function cannot be made continuous by filling in a point at x=1 .

Therefore, there is no point for removable discontinuity.

Chapter 2, Problem 25RE

Chapter 2, Problem 27RE

Chapter 2 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

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

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. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.1 - Prob. 53E Ch. 2.1 - Prob. 54E Ch. 2.1 - Prob. 55E Ch. 2.1 - Prob. 56E Ch. 2.1 - Prob. 57E Ch. 2.1 - Prob. 58E Ch. 2.1 - Prob. 59E Ch. 2.1 - Prob. 60E Ch. 2.1 - Prob. 61E Ch. 2.1 - Prob. 62E Ch. 2.1 - Prob. 63E Ch. 2.1 - Prob. 64E Ch. 2.1 - Prob. 65E Ch. 2.1 - Prob. 66E Ch. 2.1 - Prob. 67E Ch. 2.1 - Prob. 68E Ch. 2.1 - Prob. 69E Ch. 2.1 - Prob. 70E Ch. 2.1 - Prob. 71E Ch. 2.1 - Prob. 72E Ch. 2.1 - Prob. 73E Ch. 2.1 - Prob. 74E Ch. 2.1 - Prob. 75E Ch. 2.1 - Prob. 76E Ch. 2.1 - Prob. 77E Ch. 2.1 - Prob. 78E Ch. 2.1 - Prob. 79E Ch. 2.1 - Prob. 80E Ch. 2.2 - Prob. 1QR Ch. 2.2 - Prob. 2QR Ch. 2.2 - Prob. 3QR Ch. 2.2 - Prob. 4QR Ch. 2.2 - Prob. 5QR Ch. 2.2 - Prob. 6QR Ch. 2.2 - Prob. 7QR Ch. 2.2 - Prob. 8QR Ch. 2.2 - Prob. 9QR Ch. 2.2 - Prob. 10QR 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 - Prob. 20E Ch. 2.2 - Prob. 21E Ch. 2.2 - Prob. 22E Ch. 2.2 - Prob. 23E Ch. 2.2 - Prob. 24E Ch. 2.2 - Prob. 25E Ch. 2.2 - Prob. 26E Ch. 2.2 - Prob. 27E Ch. 2.2 - Prob. 28E Ch. 2.2 - Prob. 29E Ch. 2.2 - Prob. 30E Ch. 2.2 - Prob. 31E Ch. 2.2 - Prob. 32E Ch. 2.2 - Prob. 33E Ch. 2.2 - Prob. 34E Ch. 2.2 - Prob. 35E Ch. 2.2 - Prob. 36E Ch. 2.2 - Prob. 37E Ch. 2.2 - Prob. 38E Ch. 2.2 - Prob. 39E Ch. 2.2 - Prob. 40E Ch. 2.2 - Prob. 41E Ch. 2.2 - Prob. 42E Ch. 2.2 - Prob. 43E Ch. 2.2 - Prob. 44E Ch. 2.2 - Prob. 45E Ch. 2.2 - Prob. 46E Ch. 2.2 - Prob. 47E Ch. 2.2 - Prob. 48E Ch. 2.2 - Prob. 49E Ch. 2.2 - Prob. 50E Ch. 2.2 - Prob. 51E Ch. 2.2 - Prob. 52E Ch. 2.2 - Prob. 53E Ch. 2.2 - Prob. 54E Ch. 2.2 - Prob. 55E Ch. 2.2 - Prob. 56E Ch. 2.2 - Prob. 57E Ch. 2.2 - Prob. 58E Ch. 2.2 - Prob. 59E Ch. 2.2 - Prob. 60E Ch. 2.2 - Prob. 61E Ch. 2.2 - Prob. 62E Ch. 2.2 - Prob. 63E Ch. 2.2 - Prob. 64E Ch. 2.2 - Prob. 65E Ch. 2.2 - Prob. 66E Ch. 2.2 - Prob. 67E Ch. 2.2 - Prob. 68E Ch. 2.2 - Prob. 69E Ch. 2.2 - Prob. 70E Ch. 2.2 - Prob. 71E Ch. 2.2 - Prob. 1QQ Ch. 2.2 - Prob. 2QQ Ch. 2.2 - Prob. 3QQ Ch. 2.2 - Prob. 4QQ Ch. 2.3 - Prob. 1QR Ch. 2.3 - Prob. 2QR Ch. 2.3 - Prob. 3QR Ch. 2.3 - Prob. 4QR Ch. 2.3 - Prob. 5QR Ch. 2.3 - Prob. 6QR Ch. 2.3 - Prob. 7QR Ch. 2.3 - Prob. 8QR Ch. 2.3 - Prob. 9QR Ch. 2.3 - Prob. 10QR Ch. 2.3 - Prob. 1E Ch. 2.3 - Prob. 2E Ch. 2.3 - Prob. 3E Ch. 2.3 - Prob. 4E Ch. 2.3 - Prob. 5E Ch. 2.3 - Prob. 6E Ch. 2.3 - Prob. 7E Ch. 2.3 - Prob. 8E Ch. 2.3 - Prob. 9E Ch. 2.3 - Prob. 10E Ch. 2.3 - Prob. 11E Ch. 2.3 - Prob. 12E Ch. 2.3 - Prob. 13E Ch. 2.3 - Prob. 14E Ch. 2.3 - Prob. 15E Ch. 2.3 - Prob. 16E Ch. 2.3 - Prob. 17E Ch. 2.3 - Prob. 18E Ch. 2.3 - Prob. 19E Ch. 2.3 - Prob. 20E Ch. 2.3 - Prob. 21E Ch. 2.3 - Prob. 22E Ch. 2.3 - Prob. 23E Ch. 2.3 - Prob. 24E Ch. 2.3 - Prob. 25E Ch. 2.3 - Prob. 26E Ch. 2.3 - Prob. 27E Ch. 2.3 - Prob. 28E Ch. 2.3 - Prob. 29E Ch. 2.3 - Prob. 30E Ch. 2.3 - Prob. 31E Ch. 2.3 - Prob. 32E Ch. 2.3 - Prob. 33E Ch. 2.3 - Prob. 34E Ch. 2.3 - Prob. 35E Ch. 2.3 - Prob. 36E Ch. 2.3 - Prob. 37E Ch. 2.3 - Prob. 38E Ch. 2.3 - Prob. 39E Ch. 2.3 - Prob. 40E Ch. 2.3 - Prob. 41E Ch. 2.3 - Prob. 42E Ch. 2.3 - Prob. 43E Ch. 2.3 - Prob. 44E Ch. 2.3 - Prob. 45E Ch. 2.3 - Prob. 46E Ch. 2.3 - Prob. 47E Ch. 2.3 - Prob. 48E Ch. 2.3 - Prob. 49E Ch. 2.3 - Prob. 50E Ch. 2.3 - Prob. 51E Ch. 2.3 - Prob. 52E Ch. 2.3 - Prob. 53E Ch. 2.3 - Prob. 54E Ch. 2.3 - Prob. 55E Ch. 2.3 - Prob. 56E Ch. 2.3 - Prob. 57E Ch. 2.3 - Prob. 58E Ch. 2.3 - Prob. 59E Ch. 2.3 - Prob. 60E Ch. 2.3 - Prob. 61E Ch. 2.3 - Prob. 62E Ch. 2.3 - Prob. 63E Ch. 2.3 - Prob. 64E Ch. 2.4 - Prob. 1QR Ch. 2.4 - Prob. 2QR Ch. 2.4 - Prob. 3QR Ch. 2.4 - Prob. 4QR Ch. 2.4 - Prob. 5QR Ch. 2.4 - Prob. 6QR Ch. 2.4 - Prob. 7QR Ch. 2.4 - Prob. 8QR Ch. 2.4 - Prob. 9QR Ch. 2.4 - Prob. 10QR Ch. 2.4 - Prob. 1E Ch. 2.4 - Prob. 2E Ch. 2.4 - Prob. 3E Ch. 2.4 - Prob. 4E Ch. 2.4 - Prob. 5E Ch. 2.4 - Prob. 6E Ch. 2.4 - Prob. 7E Ch. 2.4 - Prob. 8E Ch. 2.4 - Prob. 9E Ch. 2.4 - Prob. 10E Ch. 2.4 - Prob. 11E Ch. 2.4 - Prob. 12E Ch. 2.4 - Prob. 13E Ch. 2.4 - Prob. 14E Ch. 2.4 - Prob. 15E Ch. 2.4 - Prob. 16E Ch. 2.4 - Prob. 17E Ch. 2.4 - Prob. 18E Ch. 2.4 - Prob. 19E Ch. 2.4 - Prob. 20E Ch. 2.4 - Prob. 21E Ch. 2.4 - Prob. 22E Ch. 2.4 - Prob. 23E Ch. 2.4 - Prob. 24E Ch. 2.4 - Prob. 25E Ch. 2.4 - Prob. 26E Ch. 2.4 - Prob. 27E Ch. 2.4 - Prob. 28E Ch. 2.4 - Prob. 29E Ch. 2.4 - Prob. 30E Ch. 2.4 - Prob. 31E Ch. 2.4 - Prob. 32E Ch. 2.4 - Prob. 33E Ch. 2.4 - Prob. 34E Ch. 2.4 - Prob. 35E Ch. 2.4 - Prob. 36E Ch. 2.4 - Prob. 37E Ch. 2.4 - Prob. 38E Ch. 2.4 - Prob. 39E Ch. 2.4 - Prob. 40E Ch. 2.4 - Prob. 41E Ch. 2.4 - Prob. 42E Ch. 2.4 - Prob. 43E Ch. 2.4 - Prob. 44E Ch. 2.4 - Prob. 45E Ch. 2.4 - Prob. 46E Ch. 2.4 - Prob. 47E Ch. 2.4 - Prob. 48E Ch. 2.4 - Prob. 49E Ch. 2.4 - Prob. 50E Ch. 2.4 - Prob. 51E Ch. 2.4 - Prob. 52E Ch. 2.4 - Prob. 53E Ch. 2.4 - Prob. 54E Ch. 2.4 - Prob. 55E Ch. 2.4 - Prob. 1QQ Ch. 2.4 - Prob. 2QQ Ch. 2.4 - Prob. 3QQ Ch. 2.4 - Prob. 4QQ Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE

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