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Math
CalculusSingle Variable Calculus: Early Transcendentals8th Edition

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Chapter 2.3, Problem 8E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
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Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).

lim t → 2 ( t 2 − 2 t 3 − 3 t + 5 ) 2

To determine

To evaluate: The limit of the function limt→2(t2−2t3−3t+5)2.

Explanation

Limit Laws:

Suppose that c is a constant and the limits limx→af(x) and limx→ag(x) exists, then

Limit law 1: limx→a[f(x)+g(x)]=limx→af(x)+limx→ag(x)

Limit law 2: limx→a[f(x)−g(x)]=limx→af(x)−limx→ag(x)

Limit law 3: limx→a[cf(x)]=climx→af(x)

Limit law 4: limx→a[f(x)g(x)]=limx→af(x)⋅limx→ag(x)

Limit law 5: limx→af(x)g(x)=limx→af(x)limx→ag(x) if limx→ag(x)≠0

Limit law 6: limx→a[f(x)]n=[limx→af(x)]n where n is a positive integer.

Limit law 7: limx→ac=c

Limit law 8: limx→ax=a

Limit law 9: limx→axn=an where n is a positive integer.

Limit law 10: limx→axn=an where n is a positive integer, if n is even, assume that a>0.

Limit law 11: limx→af(x)n=limx→af(x)n where n is a positive integer, if n is even, assume that limx→af(x)>0.

Calculation:

Obtain the limit of the function by using the limit laws as shown below.

limt→2(t2−2t3−3t+5)2=(limt→2t2−2t3−3t+5)2 (by limit law 6)=(limt→2(t2−2)limt→2(t3−3t+5))2             (by limit law 5)=(limt

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Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.2 P-1E
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