1. Given constants a and b and function u defined by u(x, y) = ay f(x² - y²) show by substitution that 1 du x əx + 1 Ju U у ду +b, holds for any differentiable function f, if b is chosen appropriately. What is this value of b?

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A: Use Hessian matrix

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Q: 3. Suppose that f is a differentiable function of one variable. If we define u(x, y) = x² f(y + In…

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Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f,(x,y) =, %3D B) f,(x, y)…

A: Power role of derivative: ddxxn=nxn-1 Derivative of function eax: ddx(eax)=aeax Given function is…

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A: Given: f(x, y)  and g(x, y) be functions of two variables with the property that ∂g∂x = ∂g∂x and…

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A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

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A: Given,            Fx,y=x2+4xy+y4-8=0

Q: 3. Let z = yg(x2 - y²) be a differentiable function. Show that z(x,y) satisfies 1 дz 10z 7 - + - = х…

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Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r - s, s² - 7r). Use the table…

A: ​gr​(7,6)=−50gs​(7,6)=93​Explanation:Step 1:​Given a Table of values of f,g and fx​,fy​​​To find:…

Q: (-) = { 2*. x 2 Find the values of a and b so that f will be differentiable at x = 2.

A: Given function is fx=7x2        ,x≤2ax+b    ,x>2. By continuity, 722=a2+b74=2a+b2a+b=28     ...1…

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Q: дz x² + y², x = 2x + 3t and y = s + t. Find and in two ways: Ət Let z = x дz əs (a) By Chain Rule.…

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Q: 10) s) =-2 -2

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A: Solution

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A: Given function is F→x,y,z=9xyj^+5xyzk^. To find:  ∇×∇×F→ Concept: Cross product formula for given…

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A: We check whether w=zez is analytic function or not.

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A: Step 1: Given that z=f(x,y),x=g(t),y=h(t) and…

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Q: 4. Make a table for each function in Question 3. a) у3 3х- 1 b) y=-0.5x + 2 c) y= 2x y y y 1 1 1 2

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Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: Let f(x, y) ƒ(2, 1) = = 150 - 2x² - 4y2. Evaluate f(2, 1). Give answer in exact form. 138

A: given  f(x,y)=150-2x2-4y2for  f(2,1) , put x=2  and y=1 in f(x,y)

Q: 3. Which of the following represent linear function? a) 3x = 20-4y b) y-4 =0 c) x' +3y = -10 d) y =…

A: The function which can be expressed in the form of Y=aX+b is called as a linear function.

Q: Find and for the functions: of Əx af ду bren 2. f(x, y) = x² − xy + y² X (x² + ² noitonut sil 4.…

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