w that every finite lattice is bounded. A lattice is called distributive if x ∨ ( y ∧ z ) = ( x ∨ y ) ∧ ( x ∨ z ) and x ∧ ( y ∨ z ) = ( x ∧ y ) ∨ ( x ∧ z ) for all x , y , and z in L .
w that every finite lattice is bounded. A lattice is called distributive if x ∨ ( y ∧ z ) = ( x ∨ y ) ∧ ( x ∨ z ) and x ∧ ( y ∨ z ) = ( x ∧ y ) ∨ ( x ∧ z ) for all x , y , and z in L .
6. Given the following graph f(x).
(-2,2)
2-
-5
-3 -2
(-2,-1)
-1
(0,1)
-2-
1
(3,0)
2 3 4 5
(3,-1)
א
X
Compute each of the following.
(a) f(-2)
(b) lim f(x)
#129
(c) lim f(x)
*→12+
(d) lim f(x)
811H
(e) f(0)
(f) lim f(x)
8011
(m) Is the function continuous at x = -2,0,3? Why or why not?
(g) lim f(x)
+0x
(h) lim f(x)
x 0
(i) f(3)
(j) lim f(x)
x-3-
(k) lim f(x)
x+3+
(1) lim f(x)
#13
(i) For a given constant a > 0, let an investor's preference be represented by the
Gaussian utility function
U(w)=1-e-aw²
For what range of wealth level w will the investor be non-satiated and risk-averse?
Explain your answer.
(ii) Give an example of a utility function that exhibits DARA and verify it.
(iii) Determine the class of utility functions with relative risk aversion coefficient
R(w)= w², w> 0.
3. Compute the profit corresponding to 12,000 units.
5. A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs $0.30 per ft2, the material for
the sides cost $0.10 per ft2, and the material for the top costs $0.20 per ft2. Letting a denote the length of one side of the base,
find a function in the variable x giving the cost of constructing the box.
6. Given the following graph f(x).
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY