The formal definition of the limit states that limc f(x) = Lif for all e> 0, there exists a ô >0 such that |f(x) - L| < e for all x with 0 < |x - c| < 6 Select the statements where the given f, c, e, and ô satisfy the formal definition of the limit. 1 1 f(x)x2, c 0, = 25 5 1 9 4, e = , c f(x) 2' 1 1, e = f(x)e-1, c ln 2' 1 f(x) 3x 5, c 2, e = 10' = 30 1 1 f(x) 3 2х + 7, с %3D — 4, є %3 100 500

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.4: Applications Of Eigenvalues And Eigenvectors
Problem 10E: Find the limit if it exists of Anx1 as n approaches infinity, where A=[02120], and x1=[aa]
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The formal definition of the limit states that limc f(x) = Lif for all e> 0, there exists a ô >0 such that |f(x) - L| < e
for all x with 0 < |x - c| < 6
Select the statements where the given f, c, e, and ô satisfy the formal definition of the limit.
1
1
f(x)x2, c 0,
=
25
5
1
9
4, e =
, c
f(x)
2'
1
1, e =
f(x)e-1, c
ln
2'
1
f(x) 3x 5, c
2, e =
10'
=
30
1
1
f(x) 3 2х + 7, с %3D — 4, є %3
100
500
Transcribed Image Text:The formal definition of the limit states that limc f(x) = Lif for all e> 0, there exists a ô >0 such that |f(x) - L| < e for all x with 0 < |x - c| < 6 Select the statements where the given f, c, e, and ô satisfy the formal definition of the limit. 1 1 f(x)x2, c 0, = 25 5 1 9 4, e = , c f(x) 2' 1 1, e = f(x)e-1, c ln 2' 1 f(x) 3x 5, c 2, e = 10' = 30 1 1 f(x) 3 2х + 7, с %3D — 4, є %3 100 500
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