Math 16B - Short Calculus
Homework 2
Instructions: Use your knowledge from 16A to help solve the following problems. On the quiz points
will only be given for correct work, not for just a correct answer. Show all steps in the solution.
1. Compute the foll

Created by Tynan Lazarus and Dawn Hess
1.1
Rules of Roots
The following rules are true for all x, y except where specied.
x2 = |x|
1 = i
x = i x
x y = xy
x
x
when y = 0
=
y
y
x3 = x x
3
x3 = x
3
x4 = x 3 x
In general:
1
x = x2
1
n
x = xn
m
n
xm

PARTIAL FRACTIONS EXAMPLE
Question: Suppose you want to make a batch of muffins, and the recipe
calls for 2 1 cups of flour. However, being a normal household, you don't have
6
any 1/6-cups. What you do have are 1/2 and 1/3 cups. What combination
of the c

Math 16B - Short Calculus
Midterm Review
Instructions: Solve the following problems. Be sure to show all your work. The exam will be closed
books and no calculator will be allowed. However, for study purposes, you should check your answers with
your class

Created by Tynan Lazarus
August 11, 2015
1.1
Basic Integrals
Let C be an arbitrary constant in the following
xn+1
+C
n+1
a dx = ax + C
xn dx =
1
sin(ax) dx = cos(ax) + C
a
cos(ax) dx =
sec(ax) tan(ax) dx =
1
csc(ax) cot(ax) dx = csc(ax) + C
a
sec2 (ax) dx

Math 16B - Short Calculus
Homework 5
Instructions: Solve the following problems. On the quiz points will only be given for correct work, not
for just a correct answer. Show all steps in the solution.
1. Compute the following antiderivatives:
(a)
(b)
(c)
(

Created by Tynan Lazarus
November 15, 2014
1.1
Basic Derivatives
Denitions of the Derivative:
f (x + h) f (x)
h0
h
d
(c) = 0
dx
lim
f (x) f (a)
xa
xa
lim
d
(x) = 1
dx
d
(cx) = c
dx
d
(cu) = c u
dx
d n
(x ) = nxn1 (Power Rule)
dx
d n
(u ) = nun1 u (Power

Math 16B - Short Calculus
Final Review Solutions
My answers may not be the same as yours. As with most problems in math, there are multiple ways to do
each problem. By doing the problem a dierent way we my end up with solution that is the same but looks
d

Math 16B - Short Calculus
Final Review
Instructions: Solve the following problems. Be sure to show all your work. The exam will be closed
books and no calculator will be allowed. However, for study purposes, you should check your answers with
your classma

Created by Tynan Lazarus and Dawn Hess
1.1
Methods of Factoring
Standard Form for quadratics is:
ax2 + bx + c
Method of nding signs
We start with
ax2 + bx + c
1
2
Case 1: If 2 is a , then our factors look like ( + )( ) or ( )( + ).
Case 2: If 2 is a +,