Solutions to QUIZ 13 (the answersheet said 14 - due to one quiz we counted as extra ;)
Problem 1: Compute the rst three terms of the following sequences:
(a) an = n! (b) an = 3n /n!
Solution(a) a1 = 1! = 1, a2 = 2! = 1 2 = 2, a3 = 3! = 1 2 3 = 6.
1
2
3
9
QUIZ 12
Name:
Problem 1: Solve by the method of your choice:
9x y = 74
Solution (one of MANY possible solutions) To get rid of x, multiply the
3x + 6y = 69
second equation by 3 and add to the rst one:
9x y = 74
9x 18y = 207
9x y = 74
19y = 133
y = 7
9x =
QUIZ 11 Solutions
Problem 1 The half-life of the radioactive element Plutonium-239 is 25,000 years.
If 10 grams of plutonium-239 are initially present, how many grams are present after
5000 years?
Solution The model of the radioactive decay is A = A0 ekt
QUIZ 8 Solutions
Problem 1
Find the vertical and horizontal asymptotes (if any), then sketch the function (compute x
and y intercepts, if possible, to make the sketch more precise):
2
(a) f (x) = x4x
2 +1
Solution. Vertical asymptotes of a rational functi
QUIZ 7
Section:
Name:
Problem 1
Consider the polynomial f (x) = (x 1)(x +3)2 . Determine its degree, x-intercepts(roots)
and their multiplicity, then sketch the function(use the LCT, and the parameter you
found above).
Solution
deg (f ) = 1 + 2 = 3.
The r
QUIZ 6
Name:
Problem 1
Sketch the graph of the function f (x) = 3x2 2x 1. Find the x and y intercepts (if
any), the axis of symmetry, the vertex coordinates, the domain and range.
Solution
(
1
The vertex: h = 22) = 3 , k = f (h) = 3 1 2 1 1 = 4 . Hence, t
MATH 241H - EXAM 1 - Solutions - September 20, 2004 1. (a) neither since b = ca and a b = 19 = 0. (b) perpendicular since a c = 0. 2. The vector from (2, 5, 3) to (3, 1, 1) is L = (1, 4, 2) so we can take (2, 5, 3) + t(1, 4, 2), giving parametric equation
MATH113 QUIZ 2 (1.3, 1.5)
1
1. Solve for b: A = 2 h(a + b)
Solution:
2A = h(a + b), b =
2A
a
h
2. You invested 15000$ in two accounts, paying 4% and 6% annual interest. You
earned 650$ in interest the rst year. Determine how much was invested at
each rate
QUIZ 3 SOLUTIONS
Problem 1
3
Solve the equation: (2x) 2 = 8
Solution The right-hand-side of the equation is 8 > 0, so we can square both sides without putting
any restrictions on the variable:
(2x)3 = 64,
now well take the cubic root of both sides:
2x = 4
QUIZ 5 Solutions
Problem 1
(a)Graph the function f (x) = x 2 1 (begin with the f (x) = x and show your
work step by step).
Description of the Solution: sketch the graph of y =
1 unit down.
x, then shift it 2 units to the right and
(b)Graph the function g
MATH 241H - EXAM 2 - Solutions - October 11, 2004 1. (a) 2/5. (b) It doesnt exist because the limit along the x-axis is 1, but the limit along the y -axis is -2. (c) f (x, 0) = 1 for all x so fx (0, 0) = 0. (d) f (0, y ) = 2 when y = 0 but f (0, 0) = 1. T
MATH 140: Exam 4
Thursday, December 6, 2007
Show all work and justify your answers. Your solutions should read nicely and be legible. They should not be composed of regurgitated fragments of your mind scattered about the page. 1. (a) Let f (x) = sin(x) an