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Assignment 2 question: Use Taylor's formula to calculate linear and quadratic approxi- mations to the function sin(Te-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.

Assignment 2 question: Use Taylor's formula to calculate linear and quadratic approxi- mations to the function sin(Te-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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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.
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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