Let X = {1, 2, 3, 4}, Y = {a, b, c}.
(1) Give an example for f : X → Y so that ∀y ∈ Y, ∃x ∈ X, f(x) =
y. 1 2
(2) Give an example for f : X → Y so that ∃y ∈ Y, ∀x ∈ X, f(x) =
y.
(3) Give an example for f : X → Y and g : Y → X so that f ◦ g =
IY
Given:
x
y
-5
1
-4
5
-3
4
-2
7
-1
10
0
8
1
9
2
13
3
14
4
13
5
18
What are the confidence limits (alpha = 0.05) for the true mean
value of Y when X = 3?
The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is
intersected by the plane 2x - y = 1. The resulting intersection is
a curve on the surface. Find a set of parametric equations for the
line tangent to this curve at the point (1,1,-23/24).
Consider the following utility function U(X,Y) = X^1/4Y^3/4
Initially
PX = 2
PY = 4
I = 120
Suppose the price of X changes to PX = 3. Perform a decomposition
and fill in the table
X
Y
Substitution Effect
Income Effect
Total Effect