CALCULUS I FALL 2015 UPDATE PAGE
SITARAMAN

Welcome.
Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,
CHECK AT LEAST ONCE A WEEK!!

SYLLABUS

Started 8/6/2015

UPDATE PAGE from Fall 2012 Calculus I with solutions to tests, quizzes, etc.,

Updated 1/4/2015
FINAL EXAM SOLUTIONS

FINAL EXAM TUE DEC 8 LKD 3116 FROM 3.30 TO 5.30 PM
NOTE CHANGE IN ROOM. It is NOT in DGH 208.

Updated 12/6/2015
I WILL GO OVER THESE TOMORROW IN REVIEW SESSION
Study these in addition to the solutions to the review problems for tests 1,2 and 3 from this course.
Then study solutions to all the tests and quizzes and practice problems from this course.

Updated 12/4/2015
TEST III SOLUTIONS
Graph of 1/(x^2+1) from problem 1 using Google
You can also get this by typing 1/(x^2+1) in the search box at WolframALpha.com

Updated 12/2/2015
Studying for final:
Study all test and quiz solutions from this semester and fall 2012 and spring 2010 semesters.
Do all practice problems from this semester.
REVIEW IN ROOM 213 ASB-B 11AM TO 1PM MONDAY DEC 7

Updated 12/2/2015
Solutions to Test 3 review problems

TEST III NEXT THURSDAY DEC 3 ; DETAILS BELOW:
Updated 11/30/2015
Practice problems for today:
5.5: 13,21,25,35,45,59,69,79,84.

Updated 11/28/2015
TEST III NEXT THURSDAY DEC 3
Study old exams from fall 2012 and spring 2010, do all practice problems (after Test I) below.
CHAPTER 4 (except 4.6 and 4.8) and CHAPTER 5 upto 5.5.
REVIEW IN CLASS ON Wed, 12/2
On Monday we will do 5.5, Integration by Substitution.
Please try this review test before coming to class on wednesday.
I will go over it then and afterwards post solutions.
It is mostly problems from fall 2012.

Updated 11/25/2015
Quiz 8 Solutions

QUIZ 8 (extra credit) on wed Nov 25; Test 3 on Thu Dec 3
QUIZ 8 on 4.4,4.5,4.7
Test 3 on all material covered after test 2.

Updated 11/23/2015
Studying for Quiz 8
Study all of Quiz 8 and problems 3, 4 of Quiz 7 from Fall 2012.
Problems 1,2,6 from test 3 of Fall 2012.
Problems 4,5,8 of test 3 from spring 2010.

A presentation of mine on Integration from Spring 2010.

Practice problems for today:
5.3: 3,9,13,21,29,31,37,39.
5.4: 2,5,9,15,31,37,43,61,69.

Updated 11/20/2015
Practice problems for today:
5.1: 5,13,21,26.
5.2: 5,19,23,37,49.

Updated 11/19/2015
Practice problems for today:
4.9: 5,15,17,25,35,41,45,53,59,61,67,75.

Updated 11/18/2015
Practice problems for today:
4.7: 31,35,37,41,45,51,74.

Updated 11/16/2015
Practice problems for today:
4.4: 59, 73, 78, 81.
4.5: 9,15,35,43, 55, 59.
4.7: 3,5,11,15,20,21,23.

Updated 11/13/2015
Practice problems for today:
4.4: 9,13,19, 17, 27, 33, 43, 47.

Updated 11/12/2015
QUIZ 7 SOLUTIONS

Updated 11/9/2015
Practice problems for today:
4.3: 11,13, 17,22,33, 43, 47, 53.

Challenge problem: 4.3 exercise 84.

Quiz 7 Thursday Nov 12, on 4.2 and 4.3
Please study quiz 7 (problems 1 and 2) of Fall 2012 (see link above for fall 2012), and last two problems of test 2 of fall 2012,
and problems 1,2 and 4 of Quiz 7 of spring 2010.

Updated 11/6/2015
Practice problems for today:
4.2: 7,9,11,17,19,21, 25,27,35,37.
Next quiz wednesday Nov 11, on 4.2 and 4.3

Updated 11/4/2015
TEST II SOLUTIONS

TEST II NEXT WEDNESDAY NOV 4
Study old exams from fall 2012 and spring 2010, do all practice problems (after Test I) below.
CHAPTERS 3 upto 3.10 and 4.1 of CHAPTER 4.
REVIEW IN CLASS ON MON, 11/2

Updated 11/2/2015
Solutions to review test

Please try this review test before coming to class on monday.
I will go over it then and afterwards post solutions.
It is mostly problems from fall 2012 and spring 2010.

Updated 10/29/2015
Practice problems for today:
4.1: 5,7,13, 25, 49, 52, 55, 57, 61, 69,73.

Updated 10/28/2015
QUIZ 6 SOLUTIONS

Quiz 6 on wednesday Oct 28
Please study practice problems from 3.7, 3.8, 3.9, 3.10
Also try problems 3,4,5 of quiz 6 and problem 3 of test 2 from fall 2012 ;
problems 3 (first part only) from quiz 7 of spring 2010 ;
problems 3,7 from test 3 of spring 2010 ;
problems 2,3 of quiz 6 of spring 2010 ;
and problems 4,5,6 of this old precalculus test

Updated 10/26/2015
Practice problems for today :
3.10: 7,13,23,33,39

Updated 10/23/2015
Practice problems for today :
3.9: 5,7,17,29,37,43

Updated 10/22/2015
Practice problems for today:
3.7: 11,13,15, 26,27, 31.
3.8: 3,5,9, 11,15,21.

Updated 10/22/2015
QUIZ 5 SOLUTIONS

Quiz 5 on wednesday Oct 21
Please study practice problems from 3.4, 3.5, 3.6
Also try all of quiz 5 from fall 2012 ; problems 8, 9 from test 2 of spring 2010 ; all of quiz 5 of spring 2010

Updated 10/19/2015
More practice problems :
3.5: 49,51,63,67.
3.6: 3,9,19,31,39,45.

Updated 10/16/2015
Practice problems for today:
3.5: 5,15,19,25,29,45.

Updated 10/15/2015
Practice problems for today:
3.4: 7,13,17,23,47,55,61,76,81,86.

Updated 10/14/2015
QUIZ 4 SOLUTIONS

Quiz 4 on wednesday Oct 14
Please study practice problems from 3.1, 3.2, 3.3
Also try quiz 4 from fall 2012 and problems 5,6,7 from test 2 of spring 2010

Updated 10/9/2015
Practice problems for today:
3.3: 9,17,22,37,51.
Today's challenge: Show that derivative of cosx is -sinx.

Updated 10/8/2015
Practice problems for today:
3.2: 7,11,23,33,43,45,51,59.
Today's challenge: 3.2 problem 62.
I have added a clarification to Test I solutions below regarding problem 2b.

Updated 10/5/2015
Practice problems for today:
3.1: 23,31,53,55,57,71,75,83.
Today's challenge:
1. Prove that e^x is the limit of (1+(x/n))^n as n goes to infinity using the fact that e is the limit of (1+(1/n))^n as n goes to infinity.
2. Plug in this limit formula for e^x in the limit for f '(0) where f(x) = e^x and show that the limit (it is actually a double limit) goes to 1.

Updated 10/2/2015
TEST I SOLUTIONS

TEST I FRIDAY 10/2
Study old exams from fall 2012 and spring 2010, do all practice problems below.
CHAPTERS 1 AND 2 AND SECTIONS OF CHAPTER 3 COVERED BY WED, SEP 30

REVIEW IN CLASS ON THU, 10/1

Updated 10/1/2015
Solutions to review test

Updated 9/29/2015
Please try this review test before coming to class on thursday.
I will go over it in class on thursday and then post solutions.
It is mostly problems from fall 2012.

Updated 9/24/2015

I have corrected a minor error in quiz 3 solutions below. Regret error.

Practice problems for today:
2.8: 3,15,23,27,29,35,51,57,59

Updated 9/23/2015
QUIZ 3 SOLUTIONS

QUIZ 3 WEDNESDAY 9/23
SECTIONS 2.5 AND 2.7

Updated 9/21/2015
Practice problems for today:
2.7: 9,13,27,33,49,51

Updated 9/18/2015
Practice problems for today:
2.5:51,57,61,62

Updated 9/17/2015
PLEASE DO PRACTICE PROBLEMS EVERY DAY
PLEASE MEET WITH ME A.S.A.P IF YOU GOT BELOW 19 IN QUIZ

Practice problems for today:
2.3: 57,58
2.5: 3,11, 15, 19, 21, 33,40, 41, 45

Updated 9/16/2015
QUIZ 2 SOLUTIONS

Study old quizzes and all practice problems from 2.1, 2.2, 2.3, 2.4 and 2.6
See updates from ALL of past week, below.

Updated 9/12/2015
If you need help best time to visit office is monday 2.30 to 4.30pm

In addition to practice problems below, do the following:
Show that limit of 1/x is 0 as x approaches infinity in the same way as we showed that 1/x approaches infinity as x approaches 0.
Namely, show that for any small quantity t, we can find x near 0 such that 1/x < t.
In other words, no line y=t above the x axis can be horizontal asymptote of y = 1/x.
It is not enough to say that 1/x keeps decreasing and is always bigger than 0. Key is to show it can get as close to 0 as we want.

Similarly show that no line y = 1-t below the line y = 1 can be a horizontal asymptote of y = 1-(1/x). [So 1-(1/x) approaches 1 as x approaches infinity].

Updated 9/11/2015
Practice problems for today:
2.1: 2,3,5,7
For 5 and 7, Instantaneous Velocity is found the same way as slope of tangent.

2.2: 5,9,31, 33, 44
For 31,33, proof is similar to that of 1/x as x goes to 0, because numerator does not go to zero. Note that dividing by highest power of x works only for limits in which x goes to infinity, where there is a horizontal asymptote. For 44 find vertical asymptotes by putting the denominator equal 0 and solving for x.

2.3: 11, 17
2.6: 19, 31

Updated 9/10/2015
Practice problems for today:
Do 19,21,23,49 from 2.2 and 15,32,44,47,49 from 2.6.
For 15 and 47 of 2.6 divide by x in both numerator and denominator to find the answer.
For 49 of 2.6 divide by x^2 (square of x) in both numerator and denominator to find the answer.

Updated 9/9/2015
Practice problems for today:
Do 47 from 2.2 and 11,12 from 2.6.

Challenge: Identify the limit in problems 47 (2.2) and 12 (2.6) as the value of a certain function at a certain number (we discussed this function in class today).

Problem 11 from 2.6 is basically the challenge problem I gave in class earlier, in which I asked you to show that the ratio of any power function to any exponential function goes to zero as x goes to infinity.

Just for your reference, the first challenge problem I gave was to find out for what values of A and B the function sin(A+Bx) would be an even function.

Updated 9/4/2015
QUIZ 1 SOLUTIONS

Updated 9/3/2015
QUIZ I ON FRIDAY 9/4.
Please bring a regular calculator! CELLPHONES NOT ALLOWED.
Based on practice problems posted everyday.
PRACTICE PROBLEMS FOR THURSDAY 9/3:
Sec 1.5:(Pages 66-68) 7,17,19,25,53,61

A Tutorial on compound interest from Khan Academy

Tutorial on exponential decay, from Khan academy

Updated 8/30/2015
PRACTICE PROBLEMS FOR MONDAY 8/31:
Sec 1.3:(Pages 44-45) 37, 49, 55
Sec 1.4:(Pages 53-55) 15, 21, 24, 31

Updated 8/28/2015
PRACTICE PROBLEMS FOR TODAY:
Sec 1.2:(Pages 34-35) 15,19
Sec 1.3:(Pages 42-45) 3,7, 17,19, 21

Supplementary material:
Two more graphs related to climate change, following up on practice problem 11 on p.20:
Graph of CO2 over past 650000 years
Graph of CO2 over past 60 years
You are welcome to check out my course Patterns in Environmental Math if you are interested in learning more.

Updated 8/27/2015
PRACTICE PROBLEMS FOR TODAY:
Sec 1.1:(Pages 21-22) 31, 35, 41, 51, 53, 65, 73, 77.

Updated 8/26/2015
PRACTICE PROBLEMS FOR TODAY:
Sec 1.1:(Pages 19-22) 7,8,9,10,11,15, 57, 59.

For our first meeting on 8/24:
Please do the diagnostic test in the textbook (just before "Preview of calculus") to make sure you are prepared for course.