Suppose that f(x, y) = 32 y at which {(x, y) | æ² + y² < 3²}.

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: Is the function f(x, y) = ||x| - |y|| - |x| - |y| differentiable at (0,0)?

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Q: Use the linear approximation of f(x) = at r = 0 to approximate f(-0.1). 1+r

A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 2x + 9y < 8. 1. Absolute minimum of f(x, y) is…

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Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 8y < 8. 1. Absolute minimum of f(x, y) is…

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Q: Suppose that f(x, y) = x² + y? at which 0 < x, y and 5x + 6y < 8. 1. Absolute minimum of f(x, y) is…

A: This question is related to linear programming, we will solve it using given information.

Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: Suppose that f(x, y) = y/x³ + 1 at which {(x, y) | 0 < y < x < 1}. %3D D

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Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

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Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

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Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

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Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: of of and ду Find f(x,y) = Vx + 3y?

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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

Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: Find given that z is a differentiable function of x and y, and xz + yz3 = 2 +x²ev

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm:…

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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Q: Suppose that f(x, y, z) = 2x + 5y + 4z at which a2 + y? + z2 < 12. 1. Absolute minimum of f(x, y, z)…

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 7y < 9. 1. Absolute minimum of f(x, y) is…

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

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Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy. Δy≈ ?

A: y=2x2+7x+4, ∆x=0.3 &amp; x=5 Differentiating with respect to x, we get dydx=22x+71+0=4x+7 Now at…

Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

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Q: 4. Let F : R² → R² defined by F(x,y) = (2x +3y, –x +y). Is F a linear? Why?

A: Given

Q: Suppose that f(x, y, z) = 3x + 3y + 4z at which a² + y² + . < 52. 1. Absolute minimum of f(x, y, z)…

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 5x + 6y < 7. 1. Absolute minimum of f(x, y) is…

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