3. Suppose that f is a differentiable function of one variable. If we define u(x, y) = x² f(y + In x), show that ди = ku ду Əx where k is a constant whose value you should determine. Hint: Let { = y + In x and consider u = x² f(£).

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

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

A:

Q: Let f(x, y) = xex²-y and P = (3,9). Calculate || Vfp||. (Express numbers in exact form. Use symbolic…

A:

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: A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both…

A: Given and Basic information:R=Rn, Revenue earned by selling 'n' tiresdollarsC=Cn, total cost of…

Q: a box with a square base and no top has a volume of 100cubic cm. If the material for the 4 sides…

A: Given that, the volume of the box is 100 cubic cm, the material cost for the 4 sides is 8 cents per…

Q: c) What is the actual revenue of the 250 000th CD player sold? (between 250000 and 250001) d) What…

A:

Q: Which values of c satisfy the conclusion of the MVT on the interval [-4, 6] if f is a linear…

A:

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: The line normal to the graph of f at the point (1,2) passes through the point (-1,1).  Which of the…

A: Topic = Functions

Q: Draw the level curves for the function f(x,y) = x2-y. Show five level curves within the limits…

A: We shall use MATLAB to solve the above problem.We are using computer code so that it will be very…

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: For what value of the Constant c is the function F defined below continuous on (-00,00)? Fly= { Y²-C…

A: A function,

Q: Let F(u, v) be a function of two variables. Let Fu(u, v) = G(u, v), and F₂(u, v) = H (u, v). Find…

A: Given:- Let Fuu,v=Gu,v and Fvu,v=Hu,v