Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 97 ppt
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 97 ppt
... instructor who prefers a thorough discussion of convergence before a discussion of the convergence of a power
series can turn to page 964 (Section 30.5), and, after completing that section, return to ... left with an expansion of the polynomial
9
The coefficients match those given by Pascal’s Triangle.
10
By the end of Section 30.5 you will be able to show that the radius o...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 5 pptx
... panda needs to take in C calories for every
pound of the panda’s weight.
i. The number of pounds of sugar cane it takes to support a panda for a day is a function
of the weight, x, of the panda. ... constants S, N, and C.
ii. The number of pounds of sugar cane it takes to support a pair of pandas, one weighing
P pounds and the other weighing Q pounds, for a period o...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 12 ppt
... details and a very readable account, consult The History of Mathematics: An Introduction, by David
Burton, McGraw-Hill Companies, Inc. 1 997.
17
Due in part to their methods of record keeping and their ... climate, the ancient Egyptians and Babylonians have
left modern historians more evidence of their mathematical development than have the people of other ancient c...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 16 pptx
... the graph of a famil-
iar function and applying appropriate shifts, flips, and stretches. Label all x- and
y-intercepts and the coordinates of any vertices and corners. Use exact values,
not numerical ... average rate of change of the function g over the interval [6, 6 + h]
C. The average rate of change of the function h over the interval [6, 6 + h]
ii. One of the func...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 19 pptx
... dollars
and quantity in thousands of units. (The equilibrium occurs when supply and
demand are equal.)
(9, 12)
16
12
p
q
supply
demand
4. A moving company charges a minimum of $250 for a move. An ... SLOPE OF A CURVE
AND INSTANTANEOUS RATE OF CHANGE
In Chapter 4 we looked at linear functions, functions characterized by a constant rate of
change. This characteristic is uni...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 21 pptx
... Calculating the Slope of a Curve and Instantaneous Rate of Change 183
the slope of the secant line through P and Q. By choosing Q successively closer to P ,
guess the slope of the tangent line at P ... Let P and Q be points on the graph of f with x-coordinates
3 and 3 + h, respectively.
(a) Sketch the graph of f and the secant lines through P and Q for h = 1 and h...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 27 ppt
... quantity of gas (in gallons) demanded for heating purposes, is given
by q = mp + b, where m and b are constants (m negative and b positive) and p is the
price of gas per gallon. The gas company ... distance.
The distance between f(x )and L is |f(x)−L|.
Similarly, the distance between x and3 is|x−3|.
Toshow that x is within some distance δ (delta for distance) of 3 but not equal...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 28 ppt
... Sketch the graph of f(t).
(b) What are the domain and range of f(t)?
7.2 LEFT- AND RIGHT-HANDED LIMITS;
SOMETIMES THE APPROACH IS CRITICAL
◆
EXAMPLE 7.10 How does f(x)=
1
x
behave as x approaches zero?
SOLUTION ... hit the value
L any number of times.
EXERCISE 7.2 Show, using the methods of Example 7.3, that lim
x→3
k = k for any constant k. Conclude
that lim
x→c
k = k for c an...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 29 ppt
... lim
x→a
f(x), try values of x close to a but not too close. And then make
your guess and take your chances. You’ll win some and you’ll lose some. But frequently,
thoughtful graphical and numerical investigation ... =−3, x = 1, and x = 5 but doesn’t take care of the removable discon-
tinuities at x =− 1and x = 0. The latter reminds us that f(a)must be defined and equal to
t...
Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 39 pptx
... a
double thickness of aluminum.
(a) Give an expression for the volume of the can.
(b) Give an expression for the amount of material used. (Remember that the top and
bottom of the can are two layers ... ?
14. A can for mandarin oranges is a cylinder with volume of 250 cubic centimeters. Denote
the radius by r and the height by h. The material used for the top and bottom is...
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