CALCULUS
I / SPRING
2011 - SECOND EXAM
0.1. Use the definition to find the derivative of the followingfunction
v'l+X.
0.2. Use implicit differentiat ion to show that the derivative of the arctangent is given
by
1
arctan x = -2
l+x
0.3. Use the rules of di
In this section were going to make sure that youre familiar with functions and function
notation. Both will appear in almost every section in a Calculus class and so you will need to be
able to deal with them.
First, what exactly is a function? An equatio
Review:ExponentialFunctions
In this section were going to review one of the more common functions in both calculus and the
sciences. However, before getting to this function lets take a much more general approach to
things.
Lets start with
Note that we av
Review:SolvingTrigEquationswithCalculators,PartII
Example 1 Solve
.
Solution
Note that the argument here is not really all that complicated but the addition of the -1 often
seems to confuse people so we need to a quick example with this kind of argument.
Review:ExponentialandLogarithmEquations
In this section well take a look at solving equations with exponential functions or logarithms in
them.
Well start with equations that involve exponential functions. The main property that well need
for these equati
Review:CommonGraphs
The purpose of this section is to make sure that youre familiar with the graphs of many of the
basic functions that youre liable to run across in a calculus class.
Example 1 Graph
.
Solution
This is a line in the slope intercept form
I
Review:LogarithmFunctions
In this section well take a look at a function that is related to the exponential functions we
looked at in the last section. We will look at logarithms in this section. Logarithms are one of
the functions that students fear the
Review:SolvingTrigEquationswithCalculators,PartI
In the previous section we started solving trig equations. The only problem with the equations
we solved in there is that they pretty much all had solutions that came from a handful of
standard angles and o
Review:SolvingTrigEquations
In this section we will take a look at solving trig equations. This is something that you will be
asked to do on a fairly regular basis in my class.
Lets just jump into the examples and see how to solve trig equations.
Example
Review:TrigFunctions
The intent of this section is to remind you of some of the more important (from a Calculus
standpoint) topics from a trig class. One of the most important (but not the first) of these
topics will be how to use the unit circle. We will
CALCULUS I / SPRING
2011 - HOMEWORK
8
0.1. Two planes flying north pass the equator at the same time and 30 miles apart. ThE
speed of th e first plane is 400mi /h and the speed of the other is 800mi /h. Find the distance
between them and the rate at which
Review for MJ
Dr.
575
Lev Simonian
(Dated: Fall , 2006)
1. Use the method of disk or washer to find the volume of the solid obtained by rotating the region bounded by
me given curves about the given axis.
= 1, y = OJabout the x-axis
b)
y2 = x3,
c) y = x3,
CALCUL US I / SPRING
2011 - SECOND
EXAM PRACTICE
0.1. Use the definition to find the derivative, at any point x
> -1, of the function
1
Answer.- The incremental quotient is
1
1
7l+Y - 7l+x
y-x
(VI+Y) (VT+X)
(y - x)
Multiplying by the conjugate the numerat
CALCULUS I / SPRING 2011 - FOURTH EXAM /'
Section: MW12 MW3 TR2A
NAME:
0.1. Find the position function X(t), of a particle moving along a straight line, with
constant acceleration equal to 2, knowing that the position and velocity vanis. t -= 2.
at
Find t
CALCULUS I / SPRING 2011 - THffiD EXAM
NAME: ,
Section: MW12 MW3 TR2A
0.1. Two small planes, fly in a collisionroute. One is 45 km North of the crossing point ,
and going South, at 225 km/h. The other is 60 krb. West of the crossing point, and going
East
CALCULUS I / SPRING 2011 - SECOND EXAM
NAME:.
Section: MW12 MW3 T R2A
0.1. 20 pts. Use the r ules of di fferentiationto find the derivative of the function
-;2)(
e
8ecause- ~e-
Date: March 24.2011.
u
CALCULUS I / SPRING 2011 - SECOND EXAM
0.2. 40 pts. Let
Continuity
Over the last few sections weve been using the term nice enough to define those functions that
we could evaluate limits by just evaluating the function at the point in question. Its now time to
formally define what we mean by nice enough.
Defin