Review
Rules of Exponents Polynomials Factoring Equations: Linear And Quadratic Graphs, Slopes, And Intercepts Exponential function Log function
Exponents
Expression of Exponents: xn x is referred to as the base; n is termed an exponent. When n is a pos
EC 470 Practice Problems for Chapters 6, 11 and 12
Zhe Yang
Spring 2017
1. Exercises p. 210 #5
2. Exercises p. 220 #6
3. Exercises p. 407 #8 9
4. Exercises p. 414 #7 8
5. Exercises p. 435 #3, 5, 7
6. Exercises p. 491 #5 6
7. Show that the function f (x, y
EC 470 Problem Set 3
Zhe Yang
Spring 2017
Due Tuesday March 7
1. A monopolist faces a nonlinear demand function Q =
5
by C(Q) = 3 + 2Q 3 .
1000
P3
and the cost function is given
(a) Write the profit function. Find M R and M C.
(b) Find the profit maximizi
EC 470 Answer Key: Problem Set 1
Zhe Yang
Spring 2017
1. (a) 26;
(b) 96;
(c) 60.
2. (a) Set A is not convex and unbounded.
(b) Set B is convex (but not strictly) and unbounded.
3. (a) f is strictly convex.
(b) g is strictly concave.
(c) f and g are both q
EC 470 Practice Problems 1
Zhe Yang
Spring 2017
1. Define f : R R by f (x) = |x 2|.
(a) Define A cfw_x|x R, f (x) 1. Is A open? closed? bounded? convex? Explain
why or why not.
(b) Define B cfw_(x, y)|x R, y < f (x). Is B open? closed? bounded? convex?
Ex
EC 470 Problem Set 1
Zhe Yang
Spring 2017
Due Tuesday January 31
1. Find the Euclidean distance between the following pairs of points:
(a) (2, 3) and (3, 2);
(b) (1, 3, 5) and (3, 1, 3);
(c) (5, 3, 1, 2) and (12, 6, 2, 3).
2. Define f : R R by f (x) = x3
EC 470 Answer Key: Problem Set 2
Zhe Yang
Spring 2017
(x+x)3 x3
x
x0
1. (a) f 0 (x) = lim
= 3x2 .
1/(x+x)2 1/x2
= 2
.
x
x3
x0
x
= 21 x .
lim x+x
x
x0
(b) f 0 (x) = lim
(c) f 0 (x) =
(x+x1)2 (x1)2
x
x0
(d) f 0 (x) = lim
2. (a) 15x2
1
x
= 2(x 1).
+ 3ex .
(
EC 470 Answer Key: Practice Problems 1
Zhe Yang
Spring 2017
1. (a) Set A is closed, bounded, and convex (not strictly).
(b) Set B is open, unbounded, and not convex.
(c) Function f is not differentiable at x = 2. f is not quasiconcave but is quasiconvex.
EC 470 Problem Set 2
Zhe Yang
Spring 2017
Due Thursday February 9
1. Use the definition of derivative to find the derivative of each function.
(a) f (x) = x3
1
x2
for x 6= 0
(c) f (x) = x for x 0
(b) f (x) =
(d) f (x) = (x 1)2
2. Use the rules of differen