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?

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: For the function of two variables defined by ƒ(u, v) = u² cos v + v² sin u, select the option that…

A: Given: Let consider the function of two variables, f(u,v)=u2cos v+ v2 sin uWe have to find ∂f∂u…

Q: 1. Let h : R → R be some twice-differentiable function. Define f(x,y) =h() for all x ≠ 0. Show that…

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Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function…

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Q: dy 4 Given the equation x + 4xy + y* = 8, evaluate Assume that the equation implicitly defines y as…

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…

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: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(6) = −4, g'(6) = −8,…

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

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)