Evaluate the limit, if it exists. lim (1/4+1/x)/(4+x) x--> -4

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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Evaluate the limit, if it exists.

lim (1/4+1/x)/(4+x)

x--> -4

Expert Solution
Step 1

The given expression is,

1
lim 4
x 4x
Step 2

This can be evaluated as,

1
1
4 x
4
lim
4x
x
lim
11
44x
4x
1 4 x
=lim
x 4x 4+x
1
= lim
4x
x-
since continuty is removed substitute the value.
1
4(4)
1
16
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