1. Find the local extremum of the function (a) f(x,y) = 2x² – xy + y² – x – 5y + 8 %3D (b) f(x,y) = xy² – 6x² – 3y² %3D -

Q: 3.4.4 Sketch the domain of integration and evaluate 2x 1-x dy (a) dx (b) Laxf d.x 2 Xx² + y²² dx dy…

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Q: Find the solution. Zy dx = (-1dx - dy) A (x-1)x = (y+1Xc - 2x - In|y-1|) B (x-1)y = (x+1Xc +x -…

A: First re-arrange the given differential equation. 2y dx=x2-1dx-dy2yx2-1=dx-dydxdydx+2yx2-1=1

Q: y" + 2y' + y = x at x = 0, y = -3, and x = 1, y = -1

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Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: 1. Consider the function f(x, y) = -3 +4xy – 2y² +3. (a) Find all critical points (b) Classify these…

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Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

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Q: Find the absolute maximum and minimum of the function f (x , y) =x² + y² on a closed triangular…

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Q: 2y dr - y dy y (x-2y) dy, y(0) =-1 O x = 2y - e +3 %3D a y = 2r- e+3 0x= 2y-e+3 O x = 3y + 2e +1

A: Given DE is 2y dx-y dy=y(x-2y)dy ⇒dx-12dy=12(x-2y)dy⇒dx=121+x-2ydy⇒dxdy=12+x2-y⇒dxdy+x-12=12-y Which…

Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Find the local maximum and minimum values and saddle point(s) of the function. (DNE if doesn't…

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Q: 6. Find a cubic function f(r) = ar³ + bx² + cx +d that has a local maximum value of 3 at r =-2 and a…

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Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x, y, z) =…

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Q: Given that y' = 2x + x²y, where y(0) = -1 with step size h=0.1. Estimate the values of y(0.2) using…

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Q: Find the Maximum and Minimum values of f(x, y,z) x +3y subject to the constrains x'+4y +z-36.

A: According to question,Given function,fx, y, z = x2 + 3y2,           ....1subject to the…

Q: The integrating factor of the non-exact DE: ydx – (x + 6y²)dy = 0 is x-2 y-2

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Q: x² +y F(x,y)=- x- y - is a homogeneous function of degree

A: Topic= Function Degree =1

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: Since y"|? v0 at x = -1/2 e we have a relative minimum at the point (c, f(c)). Substitute c = 5e¬1/2…

A: Solve it

Q: Solve the given optimization problem by using substitution. Minimize S- xy + xz + yz subject to xyz…

A: S=xy+xz+yz  =xyzz+xyzy+xyzx

Q: (ii) Find the extremum of Z= x2 +y2 subject to x + 4y 2 and examine whether the %3D %3D stationary…

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Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

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Q: g(x,y)=y-x2=0 depending on the condition f(x,y) = x2+y2-6x+9   can you find with the lagrange method…

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Q: Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical…

A: Since you have asked multiple questions, as per our policy we will answer first question. Please…

Q: 1.)(x + y - 1) * d * x - (x + 4y + 2) dy = 0

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Q: 9. (a) Use the method of Lagrange multipliers to determine the minimum and maximu values of f(x, y)…

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Q: 2. Find the particular solution of (xy + x)dx = (x?y² + x² + y² + 1)dy satisfying the initial…

A: Using Variable Separable Method

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x,y, z) = 2x²…

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Q: Find the critical point (x_0,y_0) of the function f(x,y)=(√(x2+y2))+1.

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Q: Find and classify the critical point of f(x,y) = -³y² - xy + y²³.

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Q: x² + y² F(x, y) =- - is a homogeneous function of degree

A: For finding degree of homogeneous function, Put x=hx and y=hy

Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: 7. Obtain the particular Solution by satisfying the conditions indicated. 3x dy; when x = 2, y = -1.

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Q: 3. Find a linear approximation to the function at the point x = 3. y = f(x) = x²e + 8x

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Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: Let = f(x,y) = x² -y. Use Euler's method ( with step size h = 1) to approximate the value of y(2) if…

A: The Euler method is a first-order numerical procedure for solving ordinary differential equations…

Q: Find the absolute maximum and minimum values of f(x, y)= 3+xy-x-2y on the closed triangular region…

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Q: 6. For the function y=x³, is x=0 both an inflection point and a local maximum /minimum?

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Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: O f has a relative maximum at x-a. f'(b)=0. O f"(c)>0. O f has a point of inflection at x-b.

A: The given graph is :

Q: (b) Construct the Green's function of the problem: y" +y' - 2y r(x), 0Sxs1 %3D y(0) = y'(1) = 0 %3D…

A: Given problem: y''+y'-2y=r(x),  0≤x≤1y(0)=y'(1)=0 Note: 1. Green function exists iff solution of the…

Q: Find the critical points of the function f(x,y)=x^2+y^2+6x−10y+1

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Q: 18. Find the absolute maximum and absolute minimum values for the function f (x, y) = e-**-y* (x² +…

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Q: 7.Obtain the particular solution of (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 when x = 2, y = 1

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Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

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