Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Assignment 2 question: Use Taylor's formula to calculate linear and quadratic approxi-
mations to the function
sin(Tе-²-²)
at the point (0,0). Use your formulas to make two estimates of the value of f(0.01, 0.01).
Compare the linear and quadratic estimates with the correct values. Repeat your estimate
comparisons for f(0.1,0.1), f(0.5, 0.5), and f(1,1).
How good are your estimates? What goes wrong with the approximations as you move further
from (0,0)? Sketch and label one or more contour plots to help explain your conclusions.
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Transcribed Image Text:Assignment 2 question: Use Taylor's formula to calculate linear and quadratic approxi- mations to the function sin(Tе-²-²) at the point (0,0). Use your formulas to make two estimates of the value of f(0.01, 0.01). Compare the linear and quadratic estimates with the correct values. Repeat your estimate comparisons for f(0.1,0.1), f(0.5, 0.5), and f(1,1). How good are your estimates? What goes wrong with the approximations as you move further from (0,0)? Sketch and label one or more contour plots to help explain your conclusions.
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