1. Find the maximum and minimum Valu el of on each diagonu| of the square smimum a. y=x :f (x,)= 1-maximum ; f (xy) 6.y=1-x;f(xy)=D maximumif Cx,y) O = minimum 2. Find the maximum and minimum Values of f on the entine syuare. max Min Entire squore f( x,y)=

Q: Suppose that f(x, y) = x² – xy + y° – 5x + 5y with D = {(x, y) | 0 < y <z< 5}. 1. The critical point…

A: Consider the provided question, fx,y=x2-xy+y2-5x+5y with D=x,y | 0≤y≤x≤5.differentiate fx,y w.r.t…

Q: . Let h(x, y) = x*-2xy²+2y²+7x? ) Find all critical points of h and at each critical point,…

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Q: Consider the function f(x, y) = x2 + 3y2 + 2y on the closed disk S: x2 + y2 < 1. a) Find the…

A: Consider the given function. fx,y=x2+3y2+2y (a) To fined the critical points, find the derivative…

Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm, thermal…

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Q: A clamped cubic spline S(x) on interval [0, 2] is defined by 1+ax + bx2 – 2x³ 0<x<1 1+ c(x – 1) –…

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Q: Find the maximum value of s = xy + yz + xz where x + y + z = 6.

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Q: Find the local minimum value of f(x, y) = 4+ x1 + yl – 11xy. Türkçe: f(x, y) = 4+x" + y" – 11xy…

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Q: 1. Ta)Galculate the critical polnts of Hhe function z(x, y) = K-1} + (q-3) - 5, subjet to %3D X +2y…

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Q: Suppose that f(r, y) = x² ay +y la + ly with D= {(z, y) |0<y<r < }. 1. The critical point of f(x, y)…

A: Given: f(x , y) = x2 -xy +y2 -x +y D= x ,y : 0≤y≤x≤1 To find: critical points and absolute maximum ,…

Q: Suppose that f(x, y) = x² – xy + y² – 2x + 2y with D = {(x, y) | 0 < y <¤ < 2}. %3D 1. The critical…

A: (1) Given that, f(x,y)=x2-xy+y2-2x+2y with D=x,y|0≤y≤x≤2. Take the derivative with respect to x,…

Q: Use Euler's Method with step size h=0.1 to approximate y(1.2), where y(x) satisfies the following…

A: Given initial value problem is  y'=3x+y y1=31

Q: Find the temperature u(x, t) in a rod of length L = 2 if the initial temperature is f(x) (0 < a < 1)…

A: To find - The temperature u(x,t) in a rod whose length is L=2 and if the ends are insulated from 0…

Q: 4. Find the points on x² + y² + z² = 25, %3D where the temperature T(x, y, z) = x² + 4y² + 9z², is…

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Q: The curved surface of a rod of length L is perfectly insulated against the flow of heat. The rod…

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Q: The surface of many airfoils can be described with an equation of the form Thickness max y = =…

A: As per the question we are given the general form of the equation y = f(x) of the surface of a…

Q: Find the local minimum value of f(x, y) = 4+ x'1 + yll – 11xy. Türkçe: f(x, y) = 4+ x1 + y1l – 11xy…

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Q: 2. A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x? – y² + 6y if they open…

A: Given: A cafe estimates a monthly profit, P(x, y)=27-x2-y2+6y and the region D=x, y∈ℝ2 : x2≤y≤4. To…

Q: 2 A 3 cm length silver bar with a constant cross section area 1 cm² (density 10 g/cm³, thermal…

A: Let L, K, σ and ρ denote the length, thermal conductivity, specific heat and density, respectively.…

Q: 1st Case (IBVP Summary) (ut = 1.5Uxx, 0≤x≤ 6ft, t> 0 ux(0,t) = 0, ux(6 ft,t) = 0, t> 0 (u(x,0) =…

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Q: Suppose that f(x, y) = x² – xy + y? – læ + ly with D = {(x, y) | 0 < y < x < 1}. - - 1. The critical…

A: Given: f(x,y)=x2-xy+y2-x+y. (1) Partially differentiate the function with respect to x and y…

Q: A cylindrical homogenous, isotropic rod with insulated sides has the temperature f(x) L/2 ={L-X…

A: Given that, A cylindrical homogenous, isotropic rod with the insulated sides has the temperature,…

Q: Find the local minimum value of f(x, y) = 4 + x'1 + yl1 – 11xy. Türkçe: f(x, y) = 4 + x11 + y'l –…

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Q: A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x² – y? + 6y if they open a…

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Q: 2. Consider the function S(r, y) = x²(y + 1)² + k(x + 1)²y². (a) For what value(s) of k is the point…

A: Given that    f(x,y) = x2(y+1)2 + k(x+1)2y2

Q: 5. Suppose that we have designed a cylindrical storage of radius 6 m and height 10 m, and we are…

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Q: 49.) Find the minimum distance from the point (2, 1, 4) to x + y + z = 4 by using the LaGrange…

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Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

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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: Find the local minimum value of f(x, y) = 4 + x'1 + yll – 11xy. Türkçe: f(x, y) = 4+ x1 + y11 – 11xy…

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Q: 3. To understand the spacing between fish in a school or birds in a flock, scientists have defined…

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Q: find the suprimum, in! infimum maximum and minimum of { c,1": (1+):ne w}, if t)ine w}

A: Supremum: Let A⊂ℝ then, least upper bound of the set is called supremum  of the set A. Supremum may…

Q: 1st Case (IBVP Summary) ut = 1.5uxx, 0≤x≤ 6 ft, t>0 ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) =…

A: please comment if you need any clarification. I done lots work for you.. please put thumbs up.thank…

Q: 4. Consider fCZry)= 2zy-x3y-2y? defined on square R={ tsxsl,1sys!} critical pointy Ca) How many 6f…

A: The given function is                                     f(x,y)=2xy-x2y-xy2               defined…

Q: 1. Find minimum value of f (r, y) = 2x+3y-6ry on the unit square D = {(x, y) : 0 < r, y < 1}.

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Q: Find the local minimum value of f(x, y) = 4+ x1 +yll – 11xy. Türkçe: f(x, y) = 4 + x11 + y'11 – 11xy…

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Q: Find the local minimum value of f(, y) = 4 + x° + yº – 9xy. %3D Türkçe: f(x, y) = 4+ x° + y° – 9xy…

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Q: 2. Consider the function f (x, y) = x² (y + 1)² + k(x + 1)²y². (a) For what value(s) of k is the…

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Q: A string is stretched between points x=0 and x=5. At time t = 0, the elastic medium is at rest and…

A: Given that: A string is stretched between points x=0 and x=5. At a time t=0, the elastic medium is…

Q: 4.2) Suppose you wanted to find the absolute extrema of f(x, y) = ax² + bxy+cy? + dx + ey on the…

A: The given function is, fx,y=ax2+bxy+cy2+dx+ey We have one critical point on the rectangle,…

Q: 1. Find the absolute extrema values of f(x, y) = 2x² – y? + 6y over the region R= {(x,y) E R² : x²…

A: Function in two variables can be increasing, decreasing, or constant with respect to change in value…

Q: Suppose we wish to use the Method of Lagrange Multipliers to minimize a differentiable function f(z,…

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Q: 3. a. Find and classify all critical points of f(x, y) = 5 – x³ + y³ + 3xy in R². b. Minimize f(x,…

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Q: Suppose that f(a, y) = 22 - ay + y? - a + y with D = {(2, y) | 0 <y saS 1}. 1. The critical point of…

A: Given function, fx,y=x2-xy+y2-x+y with D=x,y|0≤y≤x≤1

Q: 2. A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = = 27 – x2 – y² + 6y if they…

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Q: Find maximum and minumum values of f(x, y, z) = 5x – 10y + 25z subject to the constraint æ + y? + 22…

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Q: 20. Find the minimum value of ry+xz+ yz given that r, y, z are real numbers that satisfies the…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 4. Suppose a function y = f(x) is so be revolved at x = e from point (a,b) to (c, d), what is the…

A: If a function y=fx is rotating in the interval a, b about the x-axis. Then the formula of the…

Q: Consider the function f(x, y) = x²(y + 1)² + k(x + 1)²y². (a) For what value(s) of k is the point…

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Q: 10. Find the minimum of the integral I[y] subject to the constraint TIy) = [, s° dx = 2 JL over all…

A: Consider the problem: Extremize I[y]=∫x1x2F(x, y, y') dx subject to J[y]=∫x1x2G(x, y, y') dx=L ,…