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 2.1, Problem 56E

(a)

To determine

To find: The value of limx→b(f(x)+g(x)) .

(a)

Expert Solution

Answer to Problem 56E

The value of limx→b(f(x)+g(x)) is 4 .

Explanation of Solution

Given information: The values limx→bf(x)=7 and limx→bg(x)=−3 .

Calculation:

Use the sum property for limit.

limx→a(f(x)+g(x))=limx→a(f(x))+limx→a(g(x))

Simplify the given limit.

limx→b(f(x)+g(x))=limx→bf(x)+limx→bg(x)

Substitute 7 for limx→bf(x) and −3 for limx→bg(x) in the above expression.

limx→b(f(x)+g(x))=7+(−3)=7−3=4

Therefore, the value of limx→b(f(x)+g(x)) is 4 .

(b)

To determine

To find: The value of limx→b(f(x)⋅g(x)) .

(b)

Expert Solution

Answer to Problem 56E

The value of limx→b(f(x)⋅g(x)) is −21 .

Explanation of Solution

Given information: The values limx→bf(x)=7 and limx→bg(x)=−3 .

Calculation:

Use the product rule for limit.

limx→a(f(x)⋅g(x))=limx→a(f(x))⋅limx→a(g(x))

Simplify the given limit.

limx→b(f(x)⋅g(x))=limx→bf(x)⋅limx→bg(x)

Substitute 7 for limx→bf(x) and −3 for limx→bg(x) in the above expression.

limx→b(f(x)⋅g(x))=7×(−3)=−21

Therefore, the value of limx→b(f(x)⋅g(x)) is −21 .

(c)

To determine

To find: The value of limx→b(4g(x)) .

(c)

Expert Solution

Answer to Problem 56E

The value of limx→b(4g(x)) is −12 .

Explanation of Solution

Given information: The values limx→bf(x)=7 and limx→bg(x)=−3 .

Calculation:

Use the constant multiple rule for limit.

limx→a(kf(x))=klimx→a(f(x))

Simplify the given limit.

limx→b(4g(x))=4limx→b(g(x))

Substitute −3 for limx→b(g(x)) in the above expression.

limx→b(4g(x))=4×(−3)=−12

Therefore, the value of limx→b(4g(x)) is −12 .

(d)

To determine

To find: The value of limx→b(f(x)g(x)) .

(d)

Expert Solution

Answer to Problem 56E

The value of limx→b(f(x)g(x)) is −73 .

Explanation of Solution

Given information: The values limx→bf(x)=7 and limx→bg(x)=−3 .

Calculation:

Use the quotient rule for limit.

limx→a(f(x)g(x))=limx→a(f(x))limx→a(g(x))

Simplify the given limit.

limx→b(f(x)g(x))=limx→bf(x)limx→bg(x)

Substitute 7 for limx→b(f(x)) and −3 for limx→b(g(x)) in the above expression.

limx→b(f(x)g(x))=7−3=−73

Therefore, the value of limx→b(f(x)g(x)) is −73 .

Chapter 2.1, Problem 55E

Chapter 2.1, Problem 57E

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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The value of lim x → b ( f ( x ) + g ( x ) ) .

Concept explainers

Videos

To find: The value of limx→b(f(x)+g(x)) .

Answer to Problem 56E

Explanation of Solution

To find: The value of limx→b(f(x)⋅g(x)) .

Answer to Problem 56E

Explanation of Solution

To find: The value of limx→b(4g(x)) .

Answer to Problem 56E

Explanation of Solution

To find: The value of limx→b(f(x)g(x)) .

Answer to Problem 56E

Explanation of Solution

Chapter 2 Solutions

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