f(x, y) Let 3x² + 2y² - 2xy - 1. a Find the local maximum and minimum values and saddle points of f, if any. b) Evaluate the double integral Sp f(x, y)dA, where D = {(x, y) - 1 ≤ x ≤0, 0≤ y ≤ x²}.

Q: Let f(r, y, z) = In(r2 + 2) + y?e* – cos(2yz). Find Szya- Find all the relative extrema and saddle…

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Q: 2. Find the degree of homogeneity of the following functions: a. f(x,y) = x³ + x³y² b.x(p,r) =…

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Q: The lengths of a diameter and AB are 50 and 48, Find RP

A: Given diameter = 50 AB = 48 Hence RB = 502= 25 Also BP = 482= 24

Q: 5. f(x, y) = (y — x²)(y — 2x²). - Ans.: no extrema, saddle at (0, 0)..

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A: The given function Let

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Q: Determine fr and fy from f(x, y) = x³ + x²y + xy² + y³ ○ fx = x + xy, fy = x + 2xy ○ fx = x² + xy,…

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Q: The function f(x, y) = x2 – y² at the point (0,0) is saddle point. صواب İbi

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Q: Q1) Find the function X"(t) which minimizes the functional: 1(x) = f*([x - Subject to the boundary…

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Q: Зху? — 3x nint of r

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Q: f(x, y) = xy(3-a-y) OA. (1, В. О в. (0, 1) O C. (0,0) O P. (-3,3)

A: Given function is f(x,y)=xy(3-x-y) At first we differentiate it partially w.r.t. x and y and setting…

Q: Let g(x, y) = x4 + y² – 4x³ + 5x – 6y+3. Show that g(x,y) continuous (actually at least aC')…

A: Recall [ Implicit Function Theorem ]

Q: 3. Consider f : R2 → R defined by f(x,y) = y³ + 3x²y – 6x² – 6y? + 2. - (a) Determine the critical…

A: The given function is: f(x,y)=y3+3x2y-6x2-6y2+2

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A: Given: fx,y=ln4-x-y Objective of the given problem is to find the domain of the given function. The…

Q: 3: Let u(x, y) and v(x, y) be two twice differentiable functions such that ux = Vy, Uy Show that…

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Q: Find the global extrema of f(x, y) = x3 - xy - y2 + y on the square [0, l] x [0, 1]

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Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: Which conditions make (a, b) a critical point (stationary point) of f(x,y)? What does the sign of…

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Q: Show that the function f defined by (x, y) = (1, –1) 22 + y r + y f(x, y) = (x, y) # (1, –1) is not…

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Q: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

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Q: Let be a function that allows continuous second partial derivatives, we know that: Vf(x,y) = (16x³ -…

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Q: The shaded region is a domain for the function eq1 eq2 -1 -1 A) ƒ(x, y) = V4 – x² – y² + Vx – y² +…

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Q: Show that the function no-f 0, z = 0 f(2) = { – y* z#0 x2 + y? x² + y² is not differentiable at z =…

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Q: f (x, y) = xª – 2.x² + y² – 4y + 5. a) Use the second derivative test to find the critical points b)…

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Q: Let F(x, y, =) = (6x° In(5y² + 9) + 4=5) i + ( 10yx + 7:)j + (20xz4 + 7y – 37 sin 72) k 5y2 + 9 and…

A: To evaluate

Q: How do I get fxx, fyy, and fxy?

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Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: Compute the partial derivative fa (7,y, z) of the function f(2, y,z) = ?y yze(? u*+y*+x) + *ye(2…

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