UNIVERSITY OF WAIKATO

Department of Mathematics MATH101-10B

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Introduction to Calculus MATH101-10B*

Welcome to the home page of an Introduction to Calculus, math101. Some browsers require you to refresh this page.

Today we will continue with revision, starting with part B of the Semester B math101 final examination paper from 2009. A copy of this paper is linked here. Here also is a copy of the paper from 2010 Semester A. Other papers can be found from the University web site: iWaikato/Quick Links/Library/Exam Paper Collection.

The MathHelp facility will be available during the pre-examination study period: see the linked notice.

In addition I will be available in G3.22 Tuesday through **Thursday** 26-28th October, 2-4pm, for extra assistance if it is needed.

Test 2 scripts should be available, ground floor of block G, FCMS reception, from Friday 15th October. The test paper and solutions are linked below.

- Class web site can be found on
**http://www.math.waikato.ac.nz/~kab** - The paper outline is linked here.
- A sheet of formulas is linked here - a copy will be included with the final examination paper.
- A list of activities and occupations that use calculus is here.
- Some nice applications of mathematics are here.

Office Hours: Thursdays 3-5pm in G3.22 during teaching weeks.

- Functions: Read A&M ch 6 p49-53 Do p53 # 12,14,16(b)(c)(e)(h), 17(c),18(b),21(a),25.
- Limits of functions: Read A&M ch 7 p56-57, p58 #1,2, Do p62 #16.
- One sided and infinite limits: Read A&M ch 7 p59 # 3,4,5,6,7. Do p63 #17(a)-(d), 19 (11),(12)(13), 20, 29.
- Continuous functions: Read A&M ch 8, p66-70, Do p71 #4,8.
- Derivative: Read A&M p74 and p75#1-5, Do p77 #14(a), 16(a),18(a)(c)(d), 19(b).
- Derivative rules: Read A&M ch 10 p79 and p84 #5,14,23, Do p87 # 27, 35, 44, 51, 56.
- Chain rule: Read A&M p84 #6,7,11,12,13. Do p87 #28,34,36,38,47,48,50.
- Rates of change: Read A&M p161 p163 #1,2,3. Do p165 #10,11,12,18.
- Derivatives of trig functions: Review of trig A&M ch 16 p130-134, Read ch 17 p139-144, p145 #1,2,6,7,8,9,10. Do p149 #25(a)(b)(e)(f), 26(b),28(a),22.
- Implicit diff and related rates: Read A&M ch20 p167-170, Do p170 #9,10,14,21,22.
- Optimization and the Mean Value Theorem: Read A&M ch14 p105-108, #1,2,3,4,11,12,14. Do p115 #23,26,29,32,41.
- Higher Derivatives and the 2nd derivative test: Read A&M p98-99 p100#1,2,3,10,11,12. Do p103# 16,17,22,23(a)(iii) and (iv).
- Curve sketching, linear approximation: Read A&M ch15 p119-122, p123#1,2,6,7. Do p127 #13(b)(c)(d)(e)(f).
- Newton's method for finding roots: Read A&M ch 21 p175, p176# 5,6, Do p179 #19,21,22.
- Taylor's theorem and its applications: (1) Use the Second Mean Value Theorem to get a bound for the absolute error in the linear approximation for the square root of 9.02 using x0=9. (2) Find the Taylor approximations to f(x)=1/(1-2x) about x=0 to the higest powers of x being 1,2 and 3 and sketch the resulting polynomials on the same graph as f(x).
- Summation and Riemann sums: Read A&M Ch23, #2-5, Do p196 #6-14.
- Antiderivatives and the fundamental theorem of calculus: Read A&M ch22,24 p183 #1-8.
- Inverse functions, Inverse trig functions: Read A&M p81, Do p88 #59-64, Ch18 p152 #2,3,4,5,9,11, Do p158 #15(a)(b), 17-20, 26(a)(b)(c).
- Natural logarithm function ln and logarithmic differentiation: Read A&M p206-209, #1,4,5,6, Do p211 #1(a)(b)(c)(e)(f)(h),9(a)(d)(f), 10(a)(c).
- Exponential function: Read A&M ch26 p214-216, #1-4, Do p219 #8(a)(b)(e)(f),9(c),11(a)-(c).
- Riemann Sums application: arc length of plane curves: Read A&M p238, #7,8,9. Do p242 #13(a)-(e).
- Riemann Sums application: surface area for surfaces of revolution: Read A&M p301 , #1,2,4,5,8,9,10. Do p305 #12,13,21.
- Substitution and other techniques of integration I: Read A&M ch34 p288-291 #1-5,11,12. Do p291 #14,15,16,21,22,36.
- Substitution and other techniques of integration II: Read A&M ch34 p288-291, Do p292 #31,33,35.
- Techniques of integration II, integration by parts: Read A&M ch31 p259 and #1-9. Do p264 #14,16,18, 20, 21.
- Integration by parts II, by partial fractions I: Read A&M ch33 p279-284 #1,2,3,4. Do p286#7-11.
- Integration by partial fractions II, trig integrals: Do A&M p287 #12-16,19,23,24.
- Preparation for test 2.
- Hyperbolic functions:
Read A&M ch26 p214-219, Do p219#9(a)(d)(h)(j),10,13(a)(b),22.
## Tutorial assignments:

Your worked answers to these set problems, given below, should be handed in through the slot marked with the name of your tutor, by the given date. Please take care to select the correct slot.They will be marked and handed back during the tutorial of the following week. Late assignments cannot be accepted. Please ensure all work handed in to be marked is your own work. There are serious penalties for copying. - Tutorial 1 assignment (week of Monday 19th July for lectures 1,2,3): hand in by 11am (or 4pm in the case of William's group) Friday 23rd July: Do
A&M p53 # 14, 16(h), 18(b), p62 # 16(c), 17(b), 19(12).
- Tutorial 2 assignment (week of Monday 26th July for lectures 4,5,6) hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday
30th July. A&M p78 #18(a)(d)(use the limit definition of the derivative),p78#19(b),
p87#44, p88#51 (you can use the rule (x^n)'=nx^(n-1) where x^n means x to the power n).
- Tutorial 3 assignment (week of Monday 2nd August for lectures 7,8,9) hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday
6th August. A&M p87 #39,53, p149#20,27, p165#11.
- Tutorial 4 assignment (week of Monday 9th August relating to Lectures 10,11,12) hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday 13th August: Exercise A&M p172 # 21.
- Tutorial 5 assignment (week of Monday 16th August relating to lectures 13,14,15), hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday 13th August: p103#23(vii), p127 #13(c)(f), p179#19(c), 25.
- Tutorial 6 assignment (week of Monday 13th September relating to lectures 16-21), hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday 16th September: p159 26(c), p158#18, p197#13(d), p196#7, p212#10(a).
- Tutorial 7 assignment (week of Monday 20th September relating to lectures 22-24),
hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday 25th September: p242#13(b), p304#13, p291#14,16,21.
- Tutorial 8 assignment (week of Monday 27th September, relating to Lectures 25,26)
hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday 1st October: p292#33, p264#14,16, p286#10,11.
- Tutorial 9 assignment (week of Monday 4th October, relating to Lectures 27,28,29),
hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday 8th October:
**p287**#19, p292#30. -
**Tutorial 10 assignment**(week of Monday 11th October, relating to Lectures 30,32.) hand in by 11am (or 4pm in the case of William's 11am Friday group) Friday 15th October: p219 9(j),10(d),p291#20,p265#28&29, p276#34.## Lecture notes:

(Please note the page numbers of the links don't necessarily correspond with the page numbers on the printed lecture note pages.)- Functions and graphs: page 1, 2, 3, 4, 5, 6.
- Limits of functions: page 6b, 7, 8, 9, 10, 11, 12.
- One sided and infinite limits: page 13c, 14, 15, 16, 17, 18.
- Continuous functions: page 19, 20, 21.
- Derivative: page 22, 23, 24, 25, 26, 27, 28.
- Derivative Rules: page 29, 30, 31, 32, 33, 34.
- Chain rule: page 35, 36c, 37, 38c, 39, 40.
- Derivatives of trig functions: page 41, 42, 43, 44, 45.
- Implicit differentiation: page 46, 47, 48.
- Related Rates: page 49, 50, 51, 52, 53, 54.
- Optimization and the Mean value theorem: optimization terms, page 1, 2, 3, 4, 5.
- Higher Derivatives and the second derivative test: page 1, 2, 3, 4.
- Curve sketching, linear approx: page 1, 2, 2b, 3, 4, 5.
- Newton's method for finding roots: page 1, 2, 3, 3b, 4, 5, 6.
- Taylor's theorem and differentials: page 1, 2, 3, 3a, 3b, 4.
- Summation (new series of page numbers): page 26, 27, 28, 29, 30, 31, 32.
- Riemann sums: page 33, 34, 35, 36, 37, 38, 39.
- Dr Cavenagh's integration notes.
- Volumes using washers and shells: page 40, 41, 42, 43, 44, 45.
- Inverse functions: page 62, 63, 64, 65, 66, 67, 68, 69.
- Natural logarithm function ln, logarithmic differentiation, exponential function: page 1, 2, 3, 4, 5, 6, 7.
- Arc length of plane curves: page 46, 47, 48, 49, 50, 51, 52.
- Surface area: page 54, 55, 56, 57, 58, 59, 60, 61.
- Substitution and other techniques of integration I: page 85-1, 85-2, 85-3, 85-4, 85-5, 86, 87, 88, 89.
- Techniques of integration II, integration by parts: page 90, 91, 92, 93, 94, 95, 96, 97.
- Integration by parts, by partial fractions I: page 98, 99, 100, 101, 102, 103, 104, 105.
- Integration by partial fractions II, trig integrals: page 106, 107, 108, 109. page 110, 111, 112.
- Trigonometric substitution: 114, 115, 116, 117, 118. 119.
- Application of volumes and surface areas - light bulb problem: 127, 128, 129, 130, 131, 132, 133.
- Hyperbolic functions: 70, 71, 72, 73, 74, 75, 76.

## Tests for 2010:

- Test 1 questions, solutions.
- Test 1 makeup questions, solutions.
- Test 2 questions,
solutions.
## A test from 2009:

Questions.## Test solutions 2008:

- Test 1, 2008: questions and MC answers,, solutions for Part B.
- Test 2, 2008: questions and MC answers,, solutions for Part B.

## Example tests and solutions from 2007:

- Test 1, 2007: questions,, solutions.
- Test 2, 2007: questions,, solutions.

Kevin Broughan

14th October 2010