EX 1
EX 2
EX 3
If
find
Substitution Theorem
If f(x) is a polynomial or a rational function, then
assuming f(c) is defined.
Ex 4
Ex 5
EX 6
Hint: rationalize the numerator.
EX 1
EX 2
Find the slope of y = -x2 + 3x when x = -1, 2, and 5.
Find the equation of the tangent line to y = 2 at x=1.
x
Geometrically finding the slope of a tangent line to a curve is exactly the same
as finding the instantaneous velocity for a moving ob
Parallel and Perpendicular Lines
Parallel lines have the same slope.
Perpendicular lines have negative reciprocal slopes.
EX4
a) Find the equation of the line parallel to 3x - 4y = 8 which passes through
the point (1,3).
b) Find the equation of the line p
Ex 5
Ex 6
Definition: Right and Left Hand Limits
means that when x approaches c from the right side of c,
then f(x) is near L.
means that when x approaches c from the left side of c,
then f(x) is near L.
Theorem A
iff
Determine these limits for this funct
There is only one line between any 2 points.
The slope of a line is:
The steepness of the line.
The vertical change over the horizontal change, denoted by m.
Given two points, (x1,y1), (x2,y2) in the Cartesian Plane,
m=
Examples of slope:
EX 1
a) Find the
Consider this function:
f(x)
3.25
7.25
7.2
3.1
7.05
3.05
7.01
3.001
7.001
3
?
2.00
6.99
2.95
6.95
2.9
6.9
2.8
What happens as we approach x = 3?
x
3.2
What happens at x = 3?
6.8
So we say as x approaches 3, f(x) approaches 7.
Algebraically we compute it t
EX 4
Find the volume of the largest right circular cylinder that can be
inscribed in a sphere of radius 8m.
EX 5
A right circular cylinder is to be designed to hold a liter of water.
Find the dimensions of such a cylinder which uses the least
amount of ma
It took me 6 hours to drive 400 miles. As I drove I wrote the mileage on the trip-o-meter each
half hour. Here is a graph of my trip.
t
(miles)
d
3
Distance
170
2.5 130
2.1 112
2
time (hrs)
What was my average velocity for the trip?
vav=
What was my avera
EX 1
An open box is made from a 12" by 18" rectangular piece of cardboard
by cutting equal squares from each corner and turning up the sides.
Find the volume of the largest box that can be made in this manner.
EX 2 A Norman window is constructed by adjoin
Ex 3
A child is flying a kite. If the kite is 90 ft above the child's hand level
and the wind is blowing it on a horizontal course at 5 ft/sec, how fast
is the child letting out the cord when 150 ft of cord is out? Assume
that the cord remains straight fr
EX 1
The Ladder Problem
A 20-ft ladder is leaning against a wall. The bottom of the ladder is sliding out
from the wall at the rate of 0.5 ft per sec.
How fast is the top of the ladder sliding down the wall?
How fast is the top of the ladder sliding down