Derivatives of
Trig Functions
CALCULUS I
MRS. LOCKE
Limit Definition of Derivative
The derivative of function f at a number a
f ( a h) f ( a )
f ' (a ) lim
h 0
h
OR
f ( x) f (a)
f ' (a ) lim
x a
x a
i
Differentials, Linear and
Quadratic Approximations
CALCULUS I
MRS. LOCKE
Differentials
We will be changing our terminology
Think of dy and dx as separate quantities
called differentials
These quantiti
Using the Limit Laws
CALCULUS I
MRS. LOCKE
Review
To find the
limit of a
vector
function,
take the
limit of each
component
Limits of Vector Functions
Let r (t ) f (t ), g (t ) then
lim r (t ) lim f (t
More on Tangent
Lines & Velocity
CALCULUS I
MRS. LOCKE
Tangent Lines
Definition
A line that
touches a
curve in such
a way that
the line and
the curve
share that
point.
P(x1, y1)
P(x1, y1)
Utilizes the
Precise Definition
of a Limit
CALCULUS I
MRS. LOCKE
Limits
We want
to be able
to prove
that our
limits are
correct.
The Precise Definition
We begin to build our precise
definition of a limit by asking
Derek Ford
Lab 2
1. Given f(x) = x2 4. Graph f,f-inverse, and y = x on the same graph for x > 0.
What relationship do you notice about the graphs? On the given restricted
domain (x > 0) is f one-to-on
Maggie DiPronio
Lab 1
1. What is two raised to the power ten? 1024
2. What is the exact result of (1/2 * 3/4) + 2/7 / (3/4-1/3)? 297/280
3. What are the first 33 digits of pi? 3.1415926535897932384626
Mat 201 - Calculus One
Wolfram|Alpha Lab 9
Topic: Derivative Applications
Purpose
The purpose of this lab is to derivatives in a variety of applications. We will graph the original function along with