Explanation A limit of a function at a point a is defined as the value that the function approaches as its argument approaches point a . The notation of limit is as follows: lim x → a ( f ( x ) ) = L , which is read as “limit of f ( x ) as x approaches a is L ” One-Sided Limits: A one-sided limit is a limit that only takes into account the values of a function that approaches a value from only one side i.e. either above or below. The right-side limit of a function f as it approaches a is give as lim x → a + ( f ( x ) ) = L The left-side limit of a function f as it approaches a is give as lim x → a − ( f ( x ) ) = L If right-side limit and left-side limit of a function are the same, then a two-sided limit exists for the function. Given: A limit as lim x → 3 ( f ( x ) – 2 g ( x ) ) lim x → 3 f ( x ) = 6 and lim x → 3 g ( x ) = 4 Formula Used: 1 To determine (b) The value of the limit lim x → 3 ( x 2 f ( x ) ) if lim x → 3 f ( x ) = 6 To determine (c) The value of the limit lim x → 3 ( f ( x ) g ( x ) – x ) if lim x → 3 f ( x ) = 6 and lim x → 3 g ( x ) = 4 To determine (d) The value of the limit lim x → 3 ( 2 g ( x ) 3 - g ( x ) 3 2 ) if lim x → 3 g ( x ) = 4

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 2, Problem 64CRE

To determine

(a)

The value of the limit limx→3(f(x) – 2g(x)) if limx→3f(x) = 6 and limx→3g(x) = 4

To determine

(b)

The value of the limit limx→3(x2f(x)) if limx→3f(x) = 6

To determine

(c)

The value of the limit limx→3(f(x)g(x) – x) if limx→3f(x) = 6 and limx→3g(x) = 4

To determine

(d)

The value of the limit limx→3(2g(x)3 - g(x)32) if limx→3g(x) = 4

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Chapter 2, Problem 63CRE

Chapter 2, Problem 65CRE

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Chapter 2 Solutions

Calculus - Standalone book

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 5PQ 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. 2.2 - 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 - 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(a) The value of the limit lim x → 3 ( f ( x ) – 2 g ( x ) ) if lim x → 3 f ( x ) = 6 and lim x → 3 g ( x ) = 4

Solution Summary: The author explains that a limit is defined as the value that the function approaches as its argument approaches point a .

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(a)

The value of the limit limx→3(f(x) – 2g(x)) if limx→3f(x) = 6 and limx→3g(x) = 4

(b)

The value of the limit limx→3(x2f(x)) if limx→3f(x) = 6

(c)

The value of the limit limx→3(f(x)g(x) – x) if limx→3f(x) = 6 and limx→3g(x) = 4

(d)

The value of the limit limx→3(2g(x)3 - g(x)32) if limx→3g(x) = 4

Want to see the full answer?

Chapter 2 Solutions

(a) The value of the limit lim x → 3 ( f ( x ) – 2 g ( x ) ) if lim x → 3 f ( x ) = 6 and lim x → 3 g ( x ) = 4

Solution Summary: The author explains that a limit is defined as the value that the function approaches as its argument approaches point a .

Videos

(a) The value of the limit limx→3(f(x) – 2g(x)) if limx→3f(x) = 6 and limx→3g(x) = 4

(b) The value of the limit limx→3(x2f(x)) if limx→3f(x) = 6

(c) The value of the limit limx→3(f(x)g(x) – x) if limx→3f(x) = 6 and limx→3g(x) = 4

(d) The value of the limit limx→3(2g(x)3 - g(x)32) if limx→3g(x) = 4

Want to see the full answer?

Chapter 2 Solutions

(a)

The value of the limit limx→3(f(x) – 2g(x)) if limx→3f(x) = 6 and limx→3g(x) = 4

(b)

The value of the limit limx→3(x2f(x)) if limx→3f(x) = 6

(c)

The value of the limit limx→3(f(x)g(x) – x) if limx→3f(x) = 6 and limx→3g(x) = 4

(d)

The value of the limit limx→3(2g(x)3 - g(x)32) if limx→3g(x) = 4