2. Suppose f (x)= log(tan(1+x)). The following values for f(x) are valid. f(1.00)=-1.456916, ƒ(1.05) =-1.446183, ƒ(1.10)=-1.435709, f(1.15)=-1.42548. %3D -%3D (a) Construct a third degree Lagrange Interpolating polynomial, P,(x) using the given data. (b) Approximate f (1.07). O Determine the following absolute error: | P,(1.13) – ƒ(1.13)|.

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Chapter5: Inner Product Spaces
Section5.5: Applications Of Inner Product Spaces
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2. Suppose f (x)= log(tan(1+x)). The following values for f(x) are valid.
f(1.00)=-1.456916, ƒ(1.05) =-1.446183, ƒ(1.10)=-1.435709,
f(1.15)=-1.42548.
%3D
-%3D
(a) Construct a third degree Lagrange Interpolating polynomial, P,(x) using the given
data.
(b) Approximate f (1.07).
O Determine the following absolute error: | P,(1.13) – ƒ(1.13)|.
Transcribed Image Text:2. Suppose f (x)= log(tan(1+x)). The following values for f(x) are valid. f(1.00)=-1.456916, ƒ(1.05) =-1.446183, ƒ(1.10)=-1.435709, f(1.15)=-1.42548. %3D -%3D (a) Construct a third degree Lagrange Interpolating polynomial, P,(x) using the given data. (b) Approximate f (1.07). O Determine the following absolute error: | P,(1.13) – ƒ(1.13)|.
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