3. Consider the points X .2 .4 .6 f(x) 19867 .3894 5646 (a) Compute the Lagrange...

Transcribed Image Text:

3. Consider the points X .2 .4 .6 f(x) 19867 .3894 5646 (a) Compute the Lagrange polynomial interpolating these points (b) Use your polynomial from part (a) to approximate f(.5) (c) Compare your approximation from (b) to the actual value of f(.5)=sin(.5) (d) Compute an upper bound on the error of your approximation and compare that to the actual difference between (b) and (c). Comparing the bound to the actual error in your approximation, what do you observe? 3. Consider the points X .2 .4 .6 f(x) 19867 .3894 5646 (a) Compute the Lagrange polynomial interpolating these points (b) Use your polynomial from part (a) to approximate f(.5) (c) Compare your approximation from (b) to the actual value of f(.5)=sin(.5) (d) Compute an upper bound on the error of your approximation and compare that to the actual difference between (b) and (c). Comparing the bound to the actual error in your approximation, what do you observe?