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Assignment4
Course: MATH 241, Fall 2008School: Oregon
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#4 Assignment -- Math 241. Due: Friday, February 2. First a reminder: Exam 1, Friday, February 2. The exam will cover the material from Chapters 1 and 9 together with Sections 10.1-10.5. You will not be asked to do anything requiring your calculator, such as finding a model by regression. You may bring and use a calculator, although it shouldn't be of any use, but no crib sheets, cell phones, instant messengers,...
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#4 Assignment -- Math 241. Due: Friday, February 2.
First a reminder: Exam 1, Friday, February 2. The exam will cover the material from Chapters 1 and 9 together with Sections 10.1-10.5. You will not be asked to do anything requiring your calculator, such as finding a model by regression. You may bring and use a calculator, although it shouldn't be of any use, but no crib sheets, cell phones, instant messengers, professional or consultants. Although most of the week will be devoted to nailing down what we have learned so far, we will continue to learn more about derivatives, their significance, and their derivation. But now, in addition to getting ready for...
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Below is a small sample set of documents:
Oregon - MATH - 241
Assignment #5 - Math 241. Due: Friday, February 9.This week we shall begin serious work learning how actually to compute derivatives of familiar functions. In particular, we will learn and practice derivatives of sums, constant multiples, and powers
Oregon - MATH - 241
Assignment #6 - Math 241.Due: Friday, February 16.We continue the technical business of learning how to differentiate. For this you should aim to study, understand, and master the techniques treated in Sections 11.1, 11.2, and 11.3. It won't be all
Oregon - MATH - 241
Assignment #7 - Math 241.Due: Friday, February 23.The main focus this week will be on the applications of the derivative, Sections 12.1 and 1.2. First, though, we must take a brief look at "implicit differentiation" in Section 11.4. Most of this lat
Oregon - MATH - 241
Assignment #8 - Math 241.First of all a reminder:Due: Friday, March 2.Exam 2, Friday, 2 March. This Exam will cover the material through Section 12.2. In particular, you will be responsible for the material included in the first part of this ass
Oregon - MATH - 241
Assignment #9 - Math 241.Due: Friday, March 9.In Sections 12.2 and 12.3 we continue studying how the second derivative of a function can help us understand the behavior of that function. Moreover, particularly in Section 12.3 we'll see how the gr
Oregon - MATH - 241
Assignment #10 - Math 241.Due: Monday, March 12.First, an important reminder: FINAL EXAMINATION: 10:15-12:15, Monday, March 19This is the last assignment of the term. We will not have the opportunity have this graded and recorded, so it is not to
Oregon - MATH - 241
Some Extra Review Problems.1. Write the function f (x) = 5(7)x as an exponential in the form f (x) = Qek t. 2. Twenty grams of a radio active substance lost 6 grams from 1990 to 2005. Find its half-life and determine how much of this substance will
Oregon - MATH - 241
The Rules of Differentiation. Algebra. Addition. (f g) = f g . Multiplication by Constant. (cf ) = cf . The Product Rule. (f g) = f g + f g . The Quotient Rule. f g = f g - fg . g2Power Rule. Power Rule. d c=0 dx d a du (u ) = aua-1 dx dxa
Oregon - MATH - 241
Mathematics 241EXAMINATION IFebruary 2, 20071. [12 points] Solve each of the following equations for x: (a) ln x = 9 (b) 10x = 9 x = e9 8103. x = log10 9 0.954. x, 3 ,x 3; x > 3,2. [12 points] For the function f (x) defined by f (x)
Oregon - MATH - 241
Mathematics 241EXAMINATION IFebruary 2, 20071. [12 points] Solve each of the following equations for x: (a) ln x = 7 (b) 10x = 7 x = e7 1097. x = log10 7 0.845. 4x, 3 ,x 5; x > 5,2. [12 points] For the function f (x) defined by f (x)
Oregon - MATH - 241
Mathematics 241EXAMINATION IIMarch 2, 20071. [30 points] Find each of the following derivatives: (a) For f (x) = 6x3/2 - 7 x2d d d d 14 f (x) = f (x) = 6 (x3/2 ) - 7 (x-2 ) = 9x1/2 + 3 . dx dx dx dx x (b) For y = x3 7x + 2 dy d d 7 = (7x + 2
Oregon - MATH - 241
Mathematics 241FINAL EXAMINATION (White) SOLUTIONSMarch 19, 20071. [15 points] Find the following limits: 5 - x, if x < 1; if x = 1; (a) Given that f (x) = 4, 2 , if x > 1, x-1 (i) lim f (x) = 4x1-(ii) lim f (x) = + x1+ d 4x - 20 = (
Oregon - MATH - 241
Mathematics 241FINAL EXAMINATION (Yellow) SOLUTIONSMarch 19, 20071. [15 points] Find the following limits: 3 - x, if x < 1; if x = 1; (a) Given that f (x) = 4, 1 , if x > 1, x-1 (i) lim f (x) = 2x1-(ii) lim f (x) = + x1+ d 6x - 30 =
Oregon - MATH - 241
Syllabus. CALCULUS FOR BUSINESS AND SOCIAL SCIENCE Text: Hoffmann & Bradley, Calculus. Chapter 1. 1. Functions. 2. The graph of a function. 3. Linear functions. 4. Functional models. 5. and 6. Limits and conintuity. Remark. Sections 5 and 6 should be
Oregon - MATH - 241
CALCULUS FOR BUSINESS AND SOCIAL SCIENCE Mathematics 241 Time: 12:00-12:50 MWF + Discussion Place: 221Allen Hall Lecturer: F. W. Anderson Office: 332 Fenton Phone: 5625 e-mail anderson@math.uoregon.edu Hours: 11:00-11:50 T; 1:00-1:50 W; 2:00-2:50 F.
Oregon - MATH - 241
Functions - Linear.ALecture 1.(real-valued) function of a real variable:Rule f that assigns to each element x in a set D (the domain of f ) of real numbers a unique element, f (x) in R (the real numbers).xTEfEy = f (x)Tindependent
Oregon - MATH - 241
Exponential Models.Lecture 5.Exponential Growth. Populations, epidemics, good and bad things often experience exponential growth - or decay. For example, a species of rabbits are introduced onto a lush island and immediately behave like rabbits.
Oregon - MATH - 241
Rules of Differentiation. Product and Quotient Rules.Lecture 12.We warned earlier that we can not calculate the derivative of a product as the product of the derivatives. It is easy to see that this is so. Indeed the simple function f (x) = x2 is
Oregon - MATH - 241
Practice with Solutions.Lecture 14.Here is a copy of the first 10 problems from Lecture 14 with solutions. In most cases, we have not had time to show all the steps, just the key steps and the "answers". 1. For f (x) = x2ex, find f (x) = x2(ex) +
Oregon - MATH - 241
Implicit Differentiation.Lecture 16.We are used to working only with functions that are defined explicitly. That is, ones like 5 3 f (x) = 5x + 7x - x2 + 1 or s(t) = et -3, in which the function is described explicitly by means of a formula for
Oregon - MATH - 241
More Extrema.Lecture 18Before we leave the topic of finding extrema, we might well go through a few more examples. And even before that we might benefit from a brief review of the graphical significance of the derivative. Recall that the sign of
Oregon - MATH - 241
The Second Derivative.Lecture 19As we have seen, the derivative, f (x), of a function can provide us with very important information about the function, f (x), itself. In fact, for many problems the derivative can play a more important role than
Oregon - MATH - 241
Analyzing Graphs.Lecture 20We saw last time the information the second derivative f (x) gives us about the behavior of the function f (x). Specifically, we assembled a table telling us how the behavior of the derivative f (x) and of the second de
Oregon - MATH - 241
Related Rates.Lecture 21In practice one often encounters one of a class of problems sometimes referred to as "related rates" problems. There is nothing new mathematically. Indeed, we have actually dealt with several of these earlier, but the text
Oregon - MATH - 241
Class Review.Lecture 23We have assembled here a bunch of examples, to be worked out in class, that cover a substantial part of the new material in the entire course. Example 1. An investment of $1000 made exactly 10 years ago is now worth $2200.
Oregon - MATH - 241
Example 7. For each of the following functions find all relative maxima and relative minima, all points of inflection, and then sketch its graph: (a) f (x) = (x - 2)e-x with x 0.(b) f (x) = 2x3 - 3x2 on [-1, 2].Example 8. A rocket is fired strai
Oregon - MATH - 241
Class Review, Solutions. Here is a version of the Examples from Lecture 23 with solutions.Lecture 23Example 1. An investment of $1000 made exactly 10 years ago is now worth $2200. Assuming that it earned interest compounded continuously, (a) What
Oregon - MATH - 241
Discussion: 5p.m., Wednesday Quiz 1NAME: Math 241 January 17, 20071. [10 points] Given that y = f (x) is a linear function with f (1) = 5 and f (4) = 11 (a) Find the slope-intercept formula for f :(b) Find an equation for the function y = g(x)
Oregon - MATH - 241
Discussion: 8a.m., Thursday Quiz 2NAME: Math 241 January 25, 20071. [5 points] Given that f (x) = Abx is an exponential function and that g(x) = logc (x) is a logarithmic function, complete the following table of values: x f (x) g(x) 6 -1 1 2 4 4
Oregon - MATH - 241
Discussion: 4p.m., Wednesday Quiz 3NAME: Math 241 February 7, 20071. [8 points] Compute the derivative of the function f (x) = 4x2 - 5x3 +x+3 +7 x2. [8 points] A runner starting from a dead stop travels s(t) = 0.8t5/2 feet each second. Fi
Oregon - MATH - 241
Discussion: 8a.m., Thursday Quiz 4 Math 241NAME: February 15, 20071. [5 points] Calculate f (x) when f (x) = x(x3 - 7)8 .2. [5 points] Calculate g (t) when g(t) =5x4 + 6.3. [10 points] Given that r and s are differentiable functions of t wi