Questiona)b)x³-4xy²x²-2yLet f(x, y) =Find the first partial derivatives of f.Determine whether the limit lim f(x, y) exists or not.(x,y)-(-2,2)Determine whether the functiong(x, y) = { f(x, y), (x, y) # (0,0)-1, (x, y) = (0,0)(0,0).is continuous at the points (-2, 2) and

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Answered: Question a) b) Let f(x, y) = x³-4xy²…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = -9х + 18ху - у + 81y; (- 3, - 3), (9,9) What is the nature of the function at (- 3, - 3)? O A. f(x,y) has neither a relative maximum nor a relative minimum at (-3, - 3). B. f(x,y) has a relative maximum at (- 3, - 3). C. f(x,y) has a relative minimum at (- 3, - 3). D. The second-derivative test is inconclusive at (- 3, – 3). What is the nature of the function at (9,9)? O A. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). B. f(x,y) has a relative minimum at (9,9). O C. f(x,y) has a relative maximum at (9,9). O D. The second-derivative test is inconclusive at (9,9).
Find the partial derivative of fy for the function * 3 f (æ,y) = (3x +y) 3r² (3x² + y²)² Option 2 6y (3x² + y²)² Option 4 3y (3x² + y²)² Option 1 2 6 (3x² + y²) ² Option 3
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Find the Partial derivative of f with respect to y for * f (x, y) = x+y 2xy + y? (x + y)² (x+y) Option 2 Option 3 2.x +y 2x + y 12 (x+y)2 O Option 4 OOption 1 2.
show complete solution and use chain rule functions within functions.
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of and ду of Consider the function f(x,y) = 9x' - 4y - 2. Find -
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A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where a, b and c are real numbers. It is given that the tangent plane to the graph off at the point (−1, 3, ƒ(−1, 3)) has equation z = -6x-y-3. a) Explain why the information given tells you that f(-1, 3) = 0. b) Consider the contour line of the function f through the point (-1, 3) in the (x, y)-plane. Find the equation of the tangent line to this contour line at the point (-1, 3). You do not need to find the values for a, b and c to answer this question! c) Find the values for the numbers a, b and c.
Let f(x, y) = xsiny+ysinx+xy be given. In part (a)-(d), determine which partial derivatives the given expression? (a) cosy + cos x+1 (b) x cos y + sin x+x (c) -xsin y (d) -y sin x
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Question a) b) Let f(x, y) = x³-4xy² x²-2y Find the first partial derivatives of f. Determine whether the limit lim (x,y)-(-2,2) f(x, y) exists or not.