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Question one (a) Use the most appropriate three-point formula to determine approximations that complete the table. ( Please s
solve the error bound in part b for numerical analysis
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Answer #1

Solution,

As per given details,

f(x) = x ln(x)

f'(x)=x*\frac{1}{x}+lnx

f'(x)=1+lnx

f'(8.1)=1+ln(8.1)

= 3.091864062

error = 1.859*10-4

f'(8.3)=1+ln(8.3)

=3.116255515

error = 3.116255515 - 3.11615

= 1.055*10-4

f'(8.5)=1+ln(8.5)

= 3.140066163

f'(8.7)=1+ln(8.7)

= 3.163323026

error = 2.019*10-4

x f(x) f'(x) error
8.1 16.94410 3.09205 1.859*10-4
8.3 17.56492 3.11615 1.055*10-4
8.5 18.19056 3.139975 9.11*10-4
8.7 18.82091 3.163525 2.019*10-4
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