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

Updated 1/4/2015

FINAL EXAM SOLUTIONS

NOTE CHANGE IN ROOM. It is NOT in DGH 208.

More information below.

Updated 12/6/2015

ADDITIONAL REVIEW PROBLEMS FOR FINAL

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

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

Updated 11/30/2015

Practice problems for today:

5.5: 13,21,25,35,45,59,69,79,84.

Updated 11/28/2015

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 on 4.4,4.5,4.7

Test 3 on all material covered after test 2.

Updated 11/23/2015

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.

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

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

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

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

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

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

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

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.

Problem 11 from 2.6 is basically the

Just for your reference, the

Updated 9/4/2015

QUIZ 1 SOLUTIONS

Updated 9/3/2015

Based on practice problems posted everyday.

PRACTICE PROBLEMS FOR THURSDAY 9/3:

Sec 1.5:(Pages 66-68) 7,17,19,25,53,61

Helpful videos about exponential function, using examples from compound interest and radioactive decay:

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.

Please do the diagnostic test in the textbook (just before "Preview of calculus") to make sure you are prepared for course.