Suppose f(x)=√x is to be approximated near x=8. Find the linear approximation to f at x = 8. Then, complete the following table, showing the errors in the various approximations. Use a calculator to obtain the exact values. The percent error is calculated using the formula below. Comment on the behavior of the errors as x approaches 8. 100 approximation-exact exact Complete the linear approximation column of the table. (Round to seven decimal places as needed.) X Linear approx 8.1 8.01 8.001 8.0001 7.9999 7.999 7.99 L X 8.1 8.01 8.001 8.0001 7.9999 7.999 7.99 7.9 Linear Exact Perc approx. value err

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose fox)= x is to be approximated near x 8. Find the linear approximation to fat x= 8. Then, complete the following table, showing the errors
in the various approximations. Use a calculator to obtain the exact values. The percent error is calculated using the formula below. Comment on the
8.1
8.01
8.001
8.0001
7.9999
7.999
7.99
7.9
Linear Exact Percent
арprox. value
error
behavior of the errors as x approaches 8.
100 lapproximation - exact
lexact
Complete the linear approximation column of the table.
(Round to seven decimal places as needed.)
Linear approx
8.1
8.01
8.001
8.0001
7.9999
7.999
7.99
7.9
Transcribed Image Text:Suppose fox)= x is to be approximated near x 8. Find the linear approximation to fat x= 8. Then, complete the following table, showing the errors in the various approximations. Use a calculator to obtain the exact values. The percent error is calculated using the formula below. Comment on the 8.1 8.01 8.001 8.0001 7.9999 7.999 7.99 7.9 Linear Exact Percent арprox. value error behavior of the errors as x approaches 8. 100 lapproximation - exact lexact Complete the linear approximation column of the table. (Round to seven decimal places as needed.) Linear approx 8.1 8.01 8.001 8.0001 7.9999 7.999 7.99 7.9
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