Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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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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Question

Chapter 2, Problem 30RE

(a)

To determine

To find: The right hand and left hand limit of the given function at x=1 .

(a)

Expert Solution

Answer to Problem 30RE

The right hand limit of the function is −3 and the left hand limit of the function is 3.

Explanation of Solution

Given information: The function is f(x)={|x3−4x|, x<1x2−2x−2, x≥1 .

Calculation:

The right hand limit of the given function at x=1 can be calculated as:

limx→1+f(x)=limx→1+(x2−2x−2)=(1)2−2(1)−2=−1−2=−3

The left hand limit of the given function at x=1 can be calculated as:

limx→1−f(x)=limx→1−|x3−4x|=|(1)3−4(1)|=|−3|=3

Therefore, the right hand limit of the function is −3 and the left hand limit of the function is 3.

(b)

To determine

To check: Whether the given function has limit as x→1 .

(b)

Expert Solution

Answer to Problem 30RE

No, the given function has no limit as x→1 because the value of left hand limit and right hand limit are different.

Explanation of Solution

Given information: The function is f(x)={|x3−4x|, x<1x2−2x−2, x≥1 .

Calculation:

From part (a) at x=1 , it is calculated that the right hand limit of the given function is −3 and the left hand limit of the function is 3.

If at any point right hand limit is not equal to the left hand limit then the limit at that point does not exist. For the given function:

limx→1+f(x)≠limx→1−f(x)

Therefore, the given function has no limit as x→1 because the value of left hand limit and right hand limit are different.

(c)

To determine

To find: The points of continuity of the given function.

(c)

Expert Solution

Answer to Problem 30RE

The given function is only continuous at all point except the point x=1 .

Explanation of Solution

Given information: The function is f(x)={|x3−4x|, x<1x2−2x−2, x≥1 .

Calculation:

From part (a) at x=1 , it is calculated that the right hand limit of the given function is −3 and the left hand limit of the function is 3.

From part (b), the given function the limit as x→1 does not exist. Also, the value of left hand limit and right hand limit are different.

The function is continuous at all points except the point x=1 because at this point limit does not exist.

Therefore, the given function is only continuous at all point except the point x=1 .

(d)

To determine

To find: The points of discontinuity of the given function.

(d)

Expert Solution

Answer to Problem 30RE

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

Explanation of Solution

Given information: The function is f(x)={|x3−4x|, x<1x2−2x−2, x≥1 .

Calculation:

From part (c), it can be noticed that the given function is not continuous at point x=1 . So, the point of discontinuity is x=1 .

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

Chapter 2, Problem 29RE

Chapter 2, Problem 31RE

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic

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 - 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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 - 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The right hand and left hand limit of the given function at x = 1 .

Concept explainers

Videos

To find: The right hand and left hand limit of the given function at x=1 .

Answer to Problem 30RE

Explanation of Solution

To check: Whether the given function has limit as x→1 .

Answer to Problem 30RE

Explanation of Solution

To find: The points of continuity of the given function.

Answer to Problem 30RE

Explanation of Solution

To find: The points of discontinuity of the given function.

Answer to Problem 30RE

Explanation of Solution

Chapter 2 Solutions

Additional Math Textbook Solutions