Discrete Math Review
1. Using the predicate symbols shown and appropriate quantifiers, write each English language
statement in predicate logic. (The domain is the whole world.)
P(x) is “x is a person”
T(x) is “x is a time”
F(x1, x2) is “x1 is fooled at x2”
A. You can fool some of the people all of the time
B. You can fool all of the people some of the time
C. You can’t fool all of the people all of the time
2. Which of the following is the correct negation for “Nobody is perfect:
A. Everyone is imperfect
B. Everyone is perfect
C. Someone is perfect
4. Write the negation of the following quantified statement. Move the negation symbol as far
inside the predicate as possible. Assume that x, y, and z are all in the universe U.
$x"y"z éë( F ( x, y ) Ù G ( x, z )) ® H ( y, z ) ùû
Calculus Review
1. Evaluate lim
x®3
2x - 6
x - 4x + 3
2
sin 3x
x®0
2x
2. Find lim
3. Find the derivative of:
y=
x 2 - 3x + 2
x7 - 2
4. Find the derivative of:
y = ( 2x - 5 ) ( 3x 3 - x 2 +1)
5. Find the derivative of the function:
y = x 3 cos x - 8xsin x - 8cos x
6. Find dy of
(
y = cos 5 x
)
7. Using implicit differentiation, find
dy
of
dx
cos ( xy ) + x 7 = y 7
8. Using implicit differentiation, find
d2y
dy
and
of:
dx 2
dx
xy - x + y = 3
9. Find dy of
y = 9x 2 + 3x + 8
10. Find the second derivative of the function:
y = 3x 5 ( 3x - 4 )
2