6.(3.1) (1) Let f(x, y) = xy³+x²+y². Find fxx, fxy, fyy and evaluate them at x0 =(2) Show that f(x, y) = arctan(H)is harmonic.(2, -1).7.(3.2) Find the second order Taylor formula for the following functions at x0 = (0,0).(1) f(x, y) = tan(2x + 3y)(2) f(x, y) = ex-y²

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Answered: 6.(3.1) (1) Let f(x, y) = xy³+x²+y².…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 28E

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9. Let f be a function that has derivatives of all orders on the interval (-1,1). Assume f(0) =1, (¹) (x) ≤ 6 for all x in the interval (−1,1). ƒ'(0) = *(0) = -1, " (0)=, and (a) Find the third-degree Taylor polynomial about x = 0 for the function f.
80. The function f has derivatives of all orders for all real numbers with f(2) = -1, f'(2) = 4, ƒ"(2) = 6, and f(2) = 12. Using the third-degree Taylor polynomial for f about x = 2, what is the approximation of f(2.1)? (A) -0.570 (B) -0.568 (C) -0.566 (D) -0.528
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6.(3.1) (1) Let f(x, y) = xy³+x²+y². Find fxx, fxy, fyy and evaluate them at x0 = = (2, −1). (2) Show that f(x, y): = arctan (H) is harmonic.