Consider the function f(x)=e^(?x)cos?(2x).

Construct the Lagrange interpolating polynomial P(x) by hand using x0=0,x1=?/6,x2=?/4.

Find a bound for the absolute error on the interval [0,?/4].

Compute the absolute error at x=0.2 given by |f(0.2)?P(0.2)|. How does this error compare with the bound obtained in part (B)?

$Consider the function $ f(x)=e^{-x} \cos (2 x) $ A. Construct the Lagrange interpolating polynomial $ P(x) $ by hand usin$

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Consider the function f(x)=e^(?x)cos?(2x).

Construct the Lagrange interpolating polynomial P(x) by hand using x0=0,x1=?/6,x2=?/4.
Find a bound for the absolute error on the interval [0,?/4].
Compute the absolute error at x=0.2 given by |f(0.2)?P(0.2)|. How does this error compare with the bound obtained in part (B)?

$Consider the function $ f(x)=e^{-x} \cos (2 x) $ A. Construct the Lagrange interpolating polynomial $ P(x) $ by hand usin$

Consider the function $ f(x)=e^{-x} \cos (2 x) $ A. Construct the Lagrange interpolating polynomial $ P(x) $ by hand using $ x_{0}=0, x_{1}=\frac{\pi}{6}, x_{2}=\frac{\pi}{4} $. B. Find a bound for the absolute error on the interval $ [0, \pi / 4] $. C. Compute the absolute error at $ x=0.2 $ given by $ |f(0.2)-P(0.2)| $. How does this error compare with the bound obtained in part (B)?

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