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Q5. (a) Let f(x, y) = /1+x² + y². Find P2.(0,0)(x, y), the degree 2 Taylor polynomial of f at f(x, y) and (0, 0). = P2.(0,0)(x, y) alongside one another. plot the graphs of the surfaces z = (b) Let g(x, y) = 2+ 5x + 6xy +y². Find the degree 1 and degree 2 Taylor polynomials of g at (0,0). What do you notice? (c) Now consider a function h that is a degree 2 polynomial in x and y, i.e., h(x,y) = A+ Bx + Cy+ Dx² + Exy+ Fy², where A, B, C, D, E, F e R are constants. Make a conjecture about the degree 1 and degree 2 Taylor polynomials of h at (0,0). (d) Prove your conjecture from part (c).

Q5. (a) Let f(x, y) = /1+x² + y². Find P2.(0,0)(x, y), the degree 2 Taylor polynomial of f at f(x, y) and (0, 0). = P2.(0,0)(x, y) alongside one another. plot the graphs of the surfaces z = (b) Let g(x, y) = 2+ 5x + 6xy +y². Find the degree 1 and degree 2 Taylor polynomials of g at (0,0). What do you notice? (c) Now consider a function h that is a degree 2 polynomial in x and y, i.e., h(x,y) = A+ Bx + Cy+ Dx² + Exy+ Fy², where A, B, C, D, E, F e R are constants. Make a conjecture about the degree 1 and degree 2 Taylor polynomials of h at (0,0). (d) Prove your conjecture from part (c).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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Q5. (a) Let f(x, y) = /1+x² + y². Find P2.(0,0)(x, y), the degree 2 Taylor polynomial of f at f(x, y) and (0, 0). = P2.(0,0)(x, y) alongside one another. plot the graphs of the surfaces z = (b) Let g(x, y) = 2+ 5x + 6xy +y². Find the degree 1 and degree 2 Taylor polynomials of g at (0,0). What do you notice? (c) Now consider a function h that is a degree 2 polynomial in x and y, i.e., h(x,y) = A+ Bx + Cy + Dx² + Exy+ Fy², where A, B, C, D, E, F e R are constants. Make a conjecture about the degree 1 and degree 2 Taylor polynomials of h at (0,0). (d) Prove your conjecture from part (c).
Transcribed Image Text:Q5. (a) Let f(x, y) = /1+x² + y². Find P2.(0,0)(x, y), the degree 2 Taylor polynomial of f at f(x, y) and (0, 0). = P2.(0,0)(x, y) alongside one another. plot the graphs of the surfaces z = (b) Let g(x, y) = 2+ 5x + 6xy +y². Find the degree 1 and degree 2 Taylor polynomials of g at (0,0). What do you notice? (c) Now consider a function h that is a degree 2 polynomial in x and y, i.e., h(x,y) = A+ Bx + Cy + Dx² + Exy+ Fy², where A, B, C, D, E, F e R are constants. Make a conjecture about the degree 1 and degree 2 Taylor polynomials of h at (0,0). (d) Prove your conjecture from part (c).
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