Question

which is a one to one function

x^2=y+1

3x+2y=7

Answer #1

find y' for the function
1. (y-2)^7=3x^2+2x-2
2. 3y^3+2x^3=3
3.(4y^2+3)^4+3x^5-5=0
4. 4x^2+3x^2y^2-y^3=3x

Show that the function f(z) =x^3-3xy^2+i((3x^2y-y^3) is
differentiable

solve for x(t) and y(t):
x'=-3x+2y;
y'=-3x+4y
x(0)=0,y(0)=2

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

The real part of a f (z) complex function is given as
(x,y)=y^3-3x^2y. Show the harmonic function u(x,y) and find the
expressions v(x,y) and f(z). Calculate f'(1+2i) and write x+iy
algebraically.

Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2.
(i) Find the stationary points of f.
(ii) For each stationary point P found in (i), determine whether
f has a local maximum, a local minimum, or a saddle point at P.
Answer:
(i) (0, −2), (2, 1), (−2, 1)
(ii) (0, −2) loc. max, (± 2, 1) saddle points

Verify that the given function is the solution of the initial
value problem.
1. A) x^3y'''-3x^2y''+6xy'-6y= -(24/x) y(-1)=0 y'(-1)=0
y''(-1)=0
y=-6x-8x^2-3x^3+(1/x)
C) xy'''-y''-xy'+y^2= x^2 y(1)=2 y'(1)=5 y''(1)=-1
y=-x^2-2+2e^(x-1-e^-(x-1))+4x

Solve each system of equations
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10

solve the system of equations
1: y=3x^2-2x-1
2x+3y=2
2: x^2+(y-2)^2=4
x^2-2y=0

Using the utility function U(x,y)=3x+y/2, px=7, py=1,
and M=46 , what is the utility-maximizing demand for y,
y*?

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