Math 2 Name:_________________________________ Answer Key for Quiz 4A Review February 2015 Practice Problems
1. a. f(n) = 13n β 4 π π = β4 π = 0π π β 1 + 13 π > 0
b. f(n) = β11.5n + 49 π π = 49 π = 0π π β 1 β 11.5 π > 0
c. f(n) = 4 * 5n π π = 4 π = 0π π β 1 β 5 π > 0
d. f(n) = β3n + 8 π π = 8 π = 0π π β 1 β 3 π > 0
2. a. f(n) = 3n2 β n + 5 b. f(n) = β2n2 β 4n + 3 3. a. not a polynomial, no constant differences
b. quadratic, second order constant differences c. exponential, constant ratios
4. d(n) = n2 + 2n
5. a(n) = β4n + 12 π π = 12 π = 0π π β 1 β 4 π > 0
6. b(n) = n2 + 2n β 3 π π = β3 π = 0π π β 1 + 2π + 3 π > 0
7. c(n) = 2n3 + 1
8. d(n) = 5 * 2n π π = 5 π = 0π π β 1 β 2 π > 0
9. g(n) = β3 * 4n π π = β3 π = 0π π β 1 β 4 π > 0
Input, n Output, d(n) Ξ=2n+1 Ξ2
0 0 3 2
1 3 5 2
2 8 7 2
3 15 9 2
4 24 11 2
5 35 13
6 48