Problem 6. Describe the surface r(u, u)-R cos u x + R sin u ý + uz where 0 < u < 2π and 0 < u-H. and R and H are positive constants. What is the surface element and what is the total surface area? Show that Or/au, or/àv are continuous across the "cut at 2T coS W T
bold o solve for R Ý Solve for X 0.09x+0.08x=5.1 Solve for M m -m-231 Interval notationi -8 -2 - Graph, set builder Notater -1234-254
P X Y = + MRS= 19. Consider a consumer with preferences: u(x,y) = Ý 1 Py + In y. (a) 12 points Derive the Hicksian demands and expenditure function L = Pxx t Py Pe X +Py Ye=m PxX+ Px=m ok: Px - Aco d. Py - X J dy OL:x+ldy) - u zo 1/v/P, P,m) = m-Px + ln o ū= e-Px X (b) 4 points Verify Shephard's Lemma for this consumer. - e-Px ü
5) The velocity field for a 2D U=(x-2y)t Ň - (2x+y)t flow Ý is: a) Is this How incompressible? irrotational? 6) Find the acceleration of a Fluid element in this c) Find 0 and 4 for this flow . flow
1.) The graph of the function f(x) is given below. tr { LL Ý V Ý Ý t a. Find the intercepts of the graph. b. Find the domain and range. c. Determine the open intervals in which the function is increasing. decreasing, or constant.
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). = 2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
Q20 (5 pts). Solve the system u x 2y and vx + y for x and y and find the Jacobian( 2. Find the volume of the region R using this transformation (u,v) Q20 (5 pts). Solve the system u x 2y and vx + y for x and y and find the Jacobian( 2. Find the volume of the region R using this transformation (u,v)
Solve the system Ux = y for x. U = ? X = ? If the nxn matrix A can be expressed as A = LU, where L is a lower triangular matrix and U is an upper triangular matrix, then the system Ax = b can be expressed as LUX = b and can be solved in two steps: Step 1. Let Ux = y, so that LUX = b can be expressed as Ly = b. Solve this...
Solve u, = 4 for 0 5xs1, given u(0,t) = 0, u,(1,t) = 0, u(x,0)=1. 2 fomu sin 1 Answer: u(x,t) = { e "sin( n +) 7x 0 1 +
with u = tan(x), solve