1B AssignmentsAssignments will be posted on the Catalyst website for this course as the quarter progresses. Please check back later and check the Catalyst website. The Catalyst website will be available to enrolled students as of the start of Spring quarter.
Some assignments may be posted on this website if needed for open access (without a Catalyst ID and password).
Note about Section 4.1: You are assumed to have covered this section in Math 1A.Entering Math 1B from Math 1A, you should be capable of doing these problems from the end of section 4.1: 1- 29 odd, 39-49 odd.
If your Math 1A class did not cover section 4.1, read it and do the problems listed above. If you have questions, see the instructor during office hours (not during class) or get help at the tutorial center room S43. These important section 4.1 skills are the basis for much of our work in this course.
Section 4.2 Homework
Using Summation Notation and Formulas: 5, 7, 9, 11, 13, 19, 21, 35
Prove the following using Mathematical Induction:
*Summation Formula (ii) in Theorem 2.1 on page 356.
(Yes this is proved in the book using another method. You are asked use mathematical
induction to prove it, to practice using that technique. It is easier than if I had assigned #34!)
*Summation Formula in homework problem 33
Note: IF you are having difficulty with proof by mathematical induction and still need more practice, then redo proof done in class and the textbook for formula (iii) in Theorem 2.1 but work it through on your own, not by reading it and copying it.
IF YOU WANT TO SEE THIS ASSIGNMENT PRINTED OUT WITH THE FORMULA EQUATIONS IN IT, use the following link:
http://nebula.deanza.edu/~bloom/Math1B/1B_Section_4point2_Homework.pdf
Format for Proof by Mathematical Induction (for Sum of a Sequence)
You should have learned this in Precalculus Math 49B, but it may be a long time since you last did a proof by mathematical induction. This format sheet contains step by step instructions for learning how to do it. Consider it to be like "training wheels" for learning how to ride a bike. Use it if you need to when you practice for homework, but you must learn how to do it without this format sheet. For a quiz or exam you must know how to write it out without this.
http://nebula.deanza.edu/~bloom/Math1B/M1BProofByInductionFormat.pdf
Section 4.3 Homework is at link below
http://nebula.deanza.edu/~bloom/math1b/1B_Section_4point3_Homework.pdf
Section 4.4 Homework Part A The Definite Integral
Section 4.4 Problems 5 – 8, 11 – 14, 17, 18, 21, 22, 23, 25, 27, 28, 41, 43, 55, 56, 57
Section 4.6 #49 yes, you can do it now even though it is from section 4.6
Section 4.4 Homework Part B The Mean Value Theorem for Integrals
Problem 33: Notice the book tells you the value of the definite integral; use it to do the problem.
Revisit Problems 56, 57: FOLLOW THESE INSTRUCTIONS: For these two problems you already used geometry to evaluate the definite integral in Part A of the Section 4.4 assignment . Now use the mean value theorem for integrals to find the average value of the integrand (the function inside the integral) on the interval corresponding to the limits of integration given in the problem (interval [1,4] for #56, interval [0.2] for #57).
Section 4.5 Homework
Fundamental Theorem of Calculus Part 1
Section 4.5 Problems 7 - 20, (SKIP 21), 22, 25, 39-44, 53, 57
AND Section 4.4 problems 47 and 48
Section 4.5 Fundamental Theorem of Calculus Part 2
Section 4.5 Problems 27-32, 61
Section 4.6 Homework
Substitution is a CRUCIAL skill in Math 1B: Get lots of practice to get good at doing this and seeing what substitutions to make!
Indefinite Integrals using substitution:
1,3 (these two problems are optional but recommended as easier starting problems because the textbook suggests what substitution to use)
5 thru 8 all, 9 thru 21 odd, 23 thru 27 all
Definite integrals using substitution
31, 34, 35, 37, 38, 40
and on page 428 (Ch. 4 Review Section): 49, 52, 53, 54, 55
NOTE: In Section 4.6, IF you need more practice: appropriate problems in this section to try would be #10-22 even, 32, 33, 36. I am recommending these if you are seeking more practice because some of the that I did not assign problems later in this section are not as straightforward, so may be more difficult to understand what they are asking you to do.
Section 4.7 Homework:
Do problems 1, 3, 4, 5, 6
Note for problems 1, 3, 4: The textbook seems to like using n = 4 intervals. On the exam I may be using anything between n = 4 and n = 10 intervals, and probably more than 4. So if you need practice using more intervals, redo problems 1, 3,4 with more intervals for practice.
Do problem 13 using the online Riemann Sum calculator. Be sure that you know how to set up the sums for n=10 by hand, even if you use the online calculator to evaluate the sums.
Do problem 17, using the results for problem 13 and from our error bound worksheet that we used in class today.
Do problems 29, 33, 43
Do the under/overstatement worksheet that was handed out in class today (reverse side of error bound worksheet)
Additional homework handout (pink) for this section was given out in class and is due on Tuesday 4/28.
Section 5.1 Homework:
Area Problems: 1, 3,5-11, 19-24
Application Problems: 29-32, 37
AND ALSO the applications problems below
Section 4.4 # 49
Section 4.5 # 38
Note when you look at the graphs of the areas in section 5.1 homework problems 7 and 8, that they can easily either be done as an integral in x with vertical strips or as an integral in y with horizontal strips. Try setting it up both ways and see if you get the same answer both ways.
Section 5.2 Homework
pyramid 7
solids of revolution 17, 18, 19, 21 part b only, (SKIP 21a), 22 part b only , 23 part a only , 25, 27, 33, 36,
solids with stated cross sections 39, 41
Note: #21a was originally listed as assigned BUT has been removed from the assignment because you do not yet know how to find the antiderivative when revolving about the y axis which is what the textbook asked (until we learn more integration methods in chapter 6). Now if it had asked you to revolve it about the x axis, then the antiderivative would be easy. IF you tried #21a, set it up only, but do not evaluate it.
Section 5.3 Homework
Revolve about y axis (easiest): 3, 25b
Revolve about x- axis: 25a
Other axes of revolution: 5, 1, 9, 11, 13
Decide whether to use shells or disks and set it up using the best method, with various axes of revolution: 17, 19, 23
Section 5.4 Homework
http://nebula.deanza.edu/~bloom/Math1b/HomeworkSection5point4SmithMinton.pdf
Section 5.6 Homework
http://nebula.deanza.edu/~bloom/Math1b/HomeworkSection5point6SmithMinton.pdf
This is the same handout I gave out in class.
After class on Wed. 5/6 you are able to do the WORK problems involving TANKS and the work problems labelled GENERAL.
The work problems for springs and the center of mass problems will be covered starting Thurs. 5/7
Section 5.5 Homework
(Determining Initial Conditions: #1, 3, 4)
Vertical Projectile Motion:
#5, and also redo the same problem with an initial upward velocity of 6 ft/s
#8,9,10,13
Projectile Motion with both vertical and horizontal components
#21, 22, 25, 26, 27, 30
Link below to Section 5.7 Homework
http://nebula.deanza.edu/~bloom/math1b/1B_Section5point7.pdf
Section 6.1 Homework
1-39 odd
2-40 even are good practice also!
Section 6.2 Homework
1- 9 odd and 13 - 33 odd, 37 - 47 odd
also 4, 6, 8, 10, 62
Practice, practice, practice!!! Integration by parts becomes much easier with practice. It is only with practice that you will get good at picking u and dv. Recognizing how to pick dv involved really knowing your antiderivatives and also knowing how to do substitution so that you can "see" the appropriate clues when you look at the integral.
Note that 27, 29 and 33 are harder and will require both substitution and integration by parts.
Section 6.3 Homework Part 1: Trigonometric Integrals
(after Thursday 5/21)
1-19 odd and 8, 10, 16 AND 31
NOTE for #31, show algebraically that both answers for #31 are the same by using an appropriate identity.
Also evaluate each answer for # 31 as if the problem was a definite integral on the interval [0, pi/4] and see that the values are the same.
GENERAL NOTE: When checking answers in the back of the book, remember that answers can be equivalent but look different, and in this section it is possible that a trigonometric identity might show that your answer and the book's answer are equivalent.
Section 6.3 Homework Part 2: Trigonometric Substitution
(after Friday 5/22)
Page 529 17, 19, 23, 28
Page 529: 36 - also figure out WHY this integral gives the area of an ellipse
Page 562: 33, 34, 35
AND there were two other problems handwritten on the back of your trigonometric substitutions handout.
Section 6.4 Homework
Problems 3, 5, 9, 11, 15, 16, 20, 21, 23, 29
AND also
A1: Integral of [(x^3+2x^2+2)/(x^2+1)^2]dx
A2: Integral of (8x)/(x^2-5)dx
Section 6.6 Homework
Improper integrals with vertical asymptotes: 1, 3, 5, 7, 13, 14, 15, 25, 26, 27, 29
Improper integrals with infinite limits of integration: 9, 17, 19, 21, 23, 31, 33,
Comparison Test for Convergence or Divergence: 39, 41, 42, 43, 44, 45, 47 AND #51.
AND ALSO application problems for probability distributions (pdf): 61a,c, 63 which involving limits but not a comparison test
Section 7.1 Homework:General: 3, 5, 7,
Exponential Growth Applications: 9, 10, 11, 13,
Exponential Decay Applications: 19, 21, 23, 25, 55,
Misc Applications: 39, 45
Section 7.2 Homework:1-11 odd, 12, 13, 19, 20 ,21, 23, 25, 26, 29, 30
Application: 69
In section 7.2, we are not doing the logistic equation right now. Time permitting, we may return to do this before the end of the quarter.
Section 7.3 Homework to be determined & posted soon
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