Math 170-01 Calculus I Homework I Solutions
1. We say a function f (x) is even if f (x) = f (x), and odd if f (x) = f (x). Is it possible
for a function to be both even and odd? If not, explain why. If so, give an example of
such a function.
If such a fun
Math 280-01 Modern Algebra Exam 1 Review Solutions
1. Decide which of the following are equivalence relations on the set S . If you believe they
are, prove it by showing the properties are all satised. If you believe they are not, prove
it by showing a sp
Math 280-01 Modern Algebra Exam 2 Review Solutions
1. Explain why G = S4 and H = S6 are not isomorphic.
Since G has order 4! = 24 and H has order 6! = 720, then the two groups cannot be
isomorphic, as isomorphic groups always have the same order.
2. Write
Math 170-01 Calculus I Homework VI Solutions
1. Use logarithmic dierentiation to nd y if
y=
x3
(1 + 3x) x3 4x + 1
You do not need to simplify your answer, but it should be written entirely in terms of x.
ln(y ) = ln
x3
(1 + 3x) x3 4x + 1
= ln(x3 ) ln[(1 +
Math 170-01 Calculus I Homework IV Solutions
1. Find the equation of a line tangent to the curve f (x) = x2 8x + 9 at x = 3.
The slope of the tangent line is the value of the derivative of f at x = 3. Since
f (x) = 2x 8
then
f (3) = 2(3) 8 = 6 8 = 2
To nd
Math 170-01 Calculus I Homework III Solutions
1. Find any horizontal asymptotes, if they exist, of the functions:
(a) f (x) =
(2x 1)(x + 3)
x(x 2)
(2x 1)(x + 3)
2x2 + 5x 3
2
= lim
= =2
2 2x
x
x
x(x 2)
x
1
lim
Since the numerator and denominator are both q
Math 170-01 Calculus I Homework II Solutions
1. Assuming that a, b, c are real numbers where a2 + bc = 0, show that the function
f (x) =
ax + b
cx a
is equal to its own inverse. (Hint: compose the function with itself and simplify.)
If f (f (x) = x, then