given u=xe^y, x=a^2b, y=ab^2, what is the partial of u with respect to b (du/db)
given u=xe^y, x=a^2b, y=ab^2, what is the partial of u with respect to b (du/db)
Suppose U(x, y) = 4x2+ 3y2 1. Calculate ∂U/∂x, ∂U/∂y 2. Evaluate these partial derivatives at x= 1, y= 2 3. Calculate dy/dx for dU= 0, that is, what is the implied trade-off between x and y holding U constant? 4. Show U= 16 when x= 1, y= 2. 5. In what ratio must x and y change to hold U constant at 16 for movements away from x= 1, y= 2?
20.3 Solve the following partial differential equations for u(x, y) with the bound- cary conditions given: du . (a) x + xy = u, u= 2y on the line x = 1; b) 1 + x n = xu, u(x,0) = x.
For number 25, can someone explain to me how they got (2^(ab-b)+2^(ab-2b)+2^(ab-3b)+...+(2^(ab-ab)) and how they reached to that conclusion? For number 29, can someone explain to me how "it can't be greater than the greatest common divisor of a-b and b"? I would think that gcd(a, b) would be greater than gcd(a-b, b) because "a" and "b" are bigger than "a-b" and "b" so that confused me. Thank you! 25. Ifn e N and 2n - 1 is prime, then...
(1 point) The equations define u(x, y) and v(x, y) in terms of x and y near the point (x, y)-(1,1) and (u, v)-(1,1). Compute the partial derivatives ди du dx 0v dy dv ду Note that all answers are numbers. (1 point) The equations define u(x, y) and v(x, y) in terms of x and y near the point (x, y)-(1,1) and (u, v)-(1,1). Compute the partial derivatives ди du dx 0v dy dv ду Note that all answers...
Let f(x)-1 if XE [-1/2, 1 /2) x 2 if xE[1/2, T] If FN(x) is the partial sum of the Fourier series of f(x), then give lim Fv(1/2)? Please give your answer in decimal form. (Hint: It might be helpful to sketch the function) Let f(x)-1 if XE [-1/2, 1 /2) x 2 if xE[1/2, T] If FN(x) is the partial sum of the Fourier series of f(x), then give lim Fv(1/2)? Please give your answer in decimal form. (Hint:...
1% of pollution na lake is Db-P b) how much can be cuadh y D, 42 PIC ab na lake is Db-P b) how much can be cuadh y D, 42 PIC ab
Consider the second order partial differential equation du/dt= d^2u/dx^2 +2du/dx+u over the domain x in [0,l) and t>=0. It is given that u(0,t)=u(l,t)=0. Use the method of separation of variables to prove that the general solution with the given boundary condition is u(x,t)= infinity series n=1 bnsin(npix/l)exp(-x-((npi/l)^2)t) where bn is a constant for every n N Hint u(x,t)=X(x)T(t) tnsit te Seind ond partial difertinl cuatan +2n St the dowain e To,e) an Use metod o Separet ion Vaiades to rore...
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem) Question 2...
What is the partial derivative of log( ) with respect to y?
The flow rate between the plates is a parabola u(x,y)=U0(1-y^2/b^2) v(x,y)=0 and U0=5cm/s b=1cm viscosity u=1.0x10^-3 Ns/m^2 Find (1) y=b/2 acceleration ax=? (2) y=b/2 shear stress 2b