Practice Final Exam Problems for Ideas in Mathematics | MATH 170, Exams of Mathematics

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Practice Final 3 for Math 170 (Fall 2007)

(Math 170) Practice Midterm 3:

(1) Let Rn+1 = R n^2 + 3Rn − 2 be a mathematical model with R 0 = 1. What is R 3? (2) Let R′ n+1 = 2(R′ n)^3 − 17 R′ n be a mathematical model. How many equilibrium points does R′ n have and what are they? (3) What is 37 base 10 expressed in base 4? (4) What is 321.3 base 4 expressed in base 10? (5) Consider the mathematical model Mn+1 = M (^) n^2 + (3 − 2 i) with M 0 = 0. What is M 3? (6) What are the values of x such that x^2 − 4 x + 6 = 0? (7) What does (3 − 4 i) × (2 + i) equal? What about (3 − 4 i) + (2 + i)? (8) Let Mn+1 = (Mn)^2 + 5 be a mathematical model. How many real equilibrium points does Mn have? What (if any) are they? How many other complex equilibrium points does Mn have? What (if any) are they? (9) Which of the following pairs of functions are inverses of each other?

• f (x) = 2x + 5, g(y) = (y − 5)/ 2
• f (x) = 4x + 4, g(y) = y/ 4 − 1
• f (x) = 6x + 3, g(y) = y/ 6 − 3

• f (x) = 8x + 2, g(y) = y/ 8 − 2 (10) What is log 5 (4) to three decimal places? (11) Consider the infinite sum 1 5 +

2 +

4 +

8 +^...

Does it converge to a real number? If so what is the number? (12) Consider the infinite sum

27 + 18 + 12 + 8 +... Does it converge to a real number? If so what is the number?