Department of Mathematics and Statistics, Binghamton University

people:mckenzie:math223

2022-12-09T18:46:58-04:00

WELCOME TO MATH 223/224 INTRODUCTION TO CALCULUS/DIFFERENTIAL CALCULUS

See Math 223/224 Director's page for syllabus with grade policy and distribution of points to tests, quizzes/take-home assignments, participation, and WebAssign.

To create your WebAssign account, go to Cengage log in and register. Our class key is BINGHAMTON07007209

The e-book for Stewart's Precalculus 7e and Calculus 9e are found on the main student page in Cengage. Readings from both will be assigned; most problem sets will come from Calculus.

Exercises in Precalculus, Stewart, 7th ed. are to do in addition to the WebAssign. If they are listed it's because they focus on the skills you should have. Ask in class about any you have difficulty with.

Each week I'll desk check and sometimes collect a selection of these exercises. I'll let you know in the preceding class when I do this.

WEEK 1 AUG 24-26

Summary of assignments for first week – if an exercise gives you trouble, rest assured we'll cover them in class. These early exercises give me a broad idea of how familiar you are with fundamentals.

Exercises are to be done in a separate part of your notes. It's up to you to do them, and to have questions ready to ask in class. I will tell you ahead of time when I plan to collect a set.

Wednesday

Watch Real numbers
Read Appendix A in Calculus
In Appendix A, do #1, 5, 8, 10, 11, 25, 31, 43, 45, 49, 51
Do WebAssign warmup (you have free access until Sept 7)

Friday to Sunday

View Dr Kazmierczak's required videos and read the corresponding sections in Precalulus e-book:

Inequalities Sec 1.8

Lines Sec 1.10 Coordinate plane; graphs of equations; circles Sec 1.9

Helpful internet mini-videos on solving inequalities:

Video 1 Video 2 Video 3 Video 4

In Precalculus e-book, do Exercises Sec 1.8 #16, 18, 22, 32, 38, 47, 52, 60, 65, 79, 81, 97, 99, 113, 119 (Monday desk check only)
Lecture Notes Week 1

Go to Cengage unlimited for info on purchasing and renting the book

WEEK 2 Aug 29-Sept 2

WA schedule with some extensions to help those just getting into WA:

By Tuesday night, Appendix A and Warm-up Appendix C
By Wednesday, class time, Appendix B and Warm-up Sec 1.1
By Friday, class time, Warm-up Sec 1.2
By Friday before midnight, App C

—-

Monday-Tuesday

Do in Precalulus: Sec 1.10 (lines): #3-8 (short answer), 25, 29, 35, 37, 47, 59, 67, 77
View Graphing a circle in standard form and Completing the square to find circle equation
Do in Precalulus: Sec 1.9 (coordinate plane, circles) #7, 15, 16, 25, 85, 89, 91, 95* (we can do it in class), 99, 103

View Dr Kaz's videos, read corresponding sections in Precalulus e-book:

Rational expressions & domain Sec 1.4

Graphs of functions Sec 2.2

Getting information from a graph Sec 2.3

Transformations of functions Sec 2.6

Wednesday-Thursday

Read in Calculus e-book, Secs 1.1 & 1.2
Kazmierczak videos Equations, Quadratic fcns & models & Polynomial fcns & their graphs
Do in Calculus: Sec 1.1 (Four ways to represent functions) #39, 41, 47, 51, 53, 56 (important piecewise function), 65, 70, 81, 83, 85
Read Sec 1.2 (Mathematical models/essential fcns) #1, 4, 17, 21, 27, 28
Study Table 3: Essential fcns & their graphs (know how to sketch from memory by midterm)
Here are my own Essential fcn sketches with domains & short video to accompany it: Domain & range of 9 basic fcns
Summary of Stewart exercises so far: Precalulus Secs 1.8, 1.0, 1.10, & Calculus Secs 1.1, 1.2

Without fail, on Friday I'll do a desk check of these

Lecture notes Week 2

LABOR DAY WEEKEND

Before Tues lecture

If you need more on domain, view Domain of rational and root functions
Everyone view Odd and even functions
Read in Calculus, Sec 1.3 On fcn transformations
View Kazmierczak videos Fcn transformations (shifts) & Fcn transformations (reflections, stretches, and compressions)

WEEK 3 SEPT 6-9

WebAssigns due this week:

Class warmup Sec 1.3, due Tuesday night 9/6
Sec 1.1, due Wednesday night 9/7
Class warmup Dividing polynomials and factoring, due Thursday morning 9/8
Sec 1.2, due Thursday night 9/8
Class warmup App D, due Friday 9/9 before class, Sec 1.3, due Friday night

Tuesday

The second half of lecture today kind of fell short, in that I didn't take the time to do more combined transformations. So … I'll be adding some notes to the lecture notes and inserting them as before. And I will embellish the intro to polynomials.

Polynomial hw has been moved to Thursday night. Catch up on WebAssign.

* On the last page of Lecture notes Week 2 I've described the domains of the four composite functions. Express these in interval notation and hand in tomorrow. It's not an involved exercise!

Kazmierczak videos Dividing polynomials & Real zeros of polynomials

Wednesday-Thursday

Do exercises in Precalculus Sec 2.6 #7-51 odd (mainly short answer), 59, 63, 65, 69, 83-89 odd
Do exercises in Precalculus Sec 3.3 (dividing polynomials): #4 (can't do it with synthetic in the form it's in) 13, 17, 23, 27, 31, 39, 57, 63
Kazmierczak videos for Friday: Trigonometry of right angles, Unit circle
Division algorithm office hour video

Friday First trigonometry lecture

WEEKEND SEPT 10-11

Read App D in Calculus and for greater detail see Precalulus Secs. 5.1-2, 6.1-3
Do Exercises in Precalculus Sec 3.4 (real zeros of polynomials): #1, 5, 9, 11, 17, 31, 55, 61
Kaz video Trig fcns of real numbers
Trig exercises to start: Sec 5.1: #1, 5, 13, 17, 19, 25, 29, 47, 51 and Sec 5.2: 5-21 odd, 27-35 odd

WebAssigns due next (I've been generous with extensions of older function material, get them done)

CLASS WARMUP: Section 1.1 due Saturday night
Dividing Polynomials and Factoring due Monday night
Section 1.3 (Part 2) due Monday night Appendix D (Trigonometry)
Math 223 Midterm Review (not graded) Definitely do it by Wed class time

Lecture notes Week 3

WEEK 4 Sept 12-16

Monday New trig and review for Friday's midterm

Watch Unit circle video
UNIT CIRCLE ART HW GRADE! Create a unit circle to bring to class on Wednesday. Use a jar lid or compass to make an accurate circle and use a straight edge to make the lines. Prefer blank or copy paper to lined.
Short trig quiz on Wednesday (using unit circle you create)
Finish up Sec 5.1 and 5.2 exercises

Trigonometry exercises for the rest of the week

Textbook exercises in Calculus App. D #1, 5-11 odd, 19, 23-33 odd, 65-71 odd, 83-87 odd
Nutley H.S. solving trig eqns worksheet #1-10 (focus on sine, cosine, tangent)

Graphs are not on the quiz tomorrow, but an ability to render a graph is needed to both understand inverse functions next week and to draw trig transformations on the final).

Some of the questions here on the Previous midterm Fall 2015 and Solutions are not in our list, some are. Do the WebAssign midterm review and of course see exercises I have listed.

Midterm topics: Absolute value inequalities, quadratic or rational inequalities; write parabola or circle in standard (h,k) form to determine features and be able to graph result; transformations of essential functions and intercepts; polynomial stuff; trigonometry part 1 (anything we have done, including solving a simple trig eqn (Nutley HS).

Watch the Office hour video!. You can see some of the more recent midterm questions here, the one I can't post but did cover many items from in class and a couple here.

Friday Midterm, no lecture

—- WEEKEND SEPT 17-18

View Arc length and area of a sector of a circle
In Precalculus do Sec 6.1 Exercises #53-69 odd with arc length s = theta x r; sector area = (r²)(theta/2)
In Precalculus read Sec 2.8 (inverse fcns), Sec 5.5 (graphs of inverse trigonometric functions), and Sec 6.4 (evaluating inverse trig fcns)
View Kaz videos:

WEEK 5 Sept 19-23

Monday

First go back and do the weekend viewing; then do the arc length and sector area problems – I will post my own short video on this, as I never got a chance to talk about it in class
In Calculus read Sec 6.1 up to p 415 (skip the end of this section on derivatives!)
Sec 6.1 #17-29 odd, #37, 39
In Calculus read Sec 6.6 to p 489 (skip limits!)
View Inverse trig fcns and triangles
Try these inverse trig evaluations in Sec 6.6 #1-9 odd

Here’s my Arc length and sector area video

Wednesday

View Kazmierczak mini-videos (total viewing time is under 9 minutes!):

To hand in by email by Friday 3 pm from Nutley High School worksheet, #13, 15, and 16; be sure to show your complete work!

FRIDAY WE WILL MEET REMOTELY AT THE ZOOM LINK

Friday's quiz moved to Wednesday when we return. 5 questions total, 3 topics:

1. Determine if a fcn is even, odd, or neither using definitions 2. Find inverse of non-trigonometric fcn and graph the two fcns on one plane 3. Do three inverse trig function calculations, including a composition

WEEKEND SEPT 25

Friday Sept 23 lecture

Office hour questions on inverse trig fcns with Rui

Do these Calculus textbook exercises for Wednesday:

Trigonometry: Sec 6.6, #1-13 odd Inverse fcns: Sec 6.1 #7-13 odd, 25-29 odd Log and exp fcns: Sec. 6.2 #7, 9, 17; Sec. 6.3 #3-7 odd, 15, 17, 21, 23

WEEK 6 SEPT 28-30

Wednesday

Do these Calculus textbook exercises for Friday: Sec 6.2* #1, 3, 7, 9; Sec 6.3* #3, 5 (leave in e or ln form), 17, 21, 23; Sec 6.4* #1, 3, 7, 9

Friday-Sunday

Read in Calculus Secs 1.5 and 1.6; for more detail see Precalculus Secs 13.1 and 13.2

View Finding limits numerically and graphically and Finding limits algebraically

—- WEEK 7 OCT 3-7

Monday-Thursday All readings and exercises are in the Calculus text:

Sec 1.5, p 60, in addition to #1-18 ALL, do #27-35 odd

Read again Sec 1.6

view these: Lots of limits part 1 (with overview of techniques)

and Lots of limits part 2 (skip over the limits at infinity for now; you'll see them in 24)

Sec 1.6, p 70, do #1-31 odd (do as many as you can using the reading and video help); for class discussion, #44

By next week, getting ready for final, in Sec 6.3, p 438 do #3-11 all; #21-31 odd; 43, 47, 49-53

WEEKEND OCT 7-9

Friday-Sunday

I meant to give you this definition of vertical asymptote, which formally ties VA limit:

x = a is a vertical asymptote of f(x) is the limit as x goes to a from either direction is + or - infinity

The below video gives the same definition with several examples similar to what we did in class:

Vertical asymptotes

Lecture Notes: I re-uploaded above any that disappeared; here are the latest:

Lecture notes week 5 Lecture notes week 7 part 1 and Lecture notes week 7 part 2

Complete the WebAssignments by tonight, please. Continue working out the limit exercises. If WA asks for limits at infinity, you may omit those, but let me know.

Start working on Math 223 Fall 2015 Final and Math 223 Fall 2016 Final for practice

Read Sec 1.8, continuity

WEEK 8

Wednesday class will be at this Zoom link

View Limits and continuity

In Sec 1.6, p 70, do these further limit exercises #33, 44*, 45, 51, 54*

In Sec 1.8, do continuity exercises #3, 7-27 odd, 39-48 all, #54-58 all

You may like a complete overview of limits, view Intro to limits, Properties of limits (kind of tedious, but some good examples), and Determinng limits

On Friday you’ll have a Math 223 skills quiz. Today, Wednesday, is the zoom class.

Wednesday Here is Today's zoom lecture recording

Besides studying for the final exam, prepare for the Math 223 skills quiz on Friday, which will be these topics:

Domain of function
Essential graphs, including graphing an absolute value transformation (like we did today)
Factoring, including special factors
Evaluating trig expressions
Evaluating log and exponential expressions
Finding intercepts of circles and parabolas
Basic limits

Practice quiz page 1

Practice quiz page 2

Key to practice skills quiz page 1

Key page 2

Key graphs

Lecture Notes (recent) from Rui

Sunday Oct 16

Solutions to Fall 2015 final

Solutions to Fall 2016 final

WEEK 9 HERE IS WHERE MATH 224 BEGINS

Monday Review limits and continuity homework, readings and videos. For the new folks, here was the WEEK 8 homework. For the continuing students, this is a good time to go back and do the text exercises you might have 'missed'

Read in Calculus Secs 1.5 and 1.6; for more detail see Precalculus Secs 13.1 and 13.2

View Finding limits numerically and graphically and Finding limits algebraically

Do Sec 1.5 p 60, #1-18 ALL, do #27-35 odd and Sec 1.6, p 70, do #1-31 odd, #33, 44*, 45, 51, 54*

View these: Lots of limits part 1 (with overview of techniques)

and Lots of limits part 2 (skip over the limits at infinity for now; you'll see them in 24)

Lecture Notes: I re-uploaded above any that disappeared; here are the latest:

Lecture notes week 5 Lecture notes week 7 part 1 and Lecture notes week 7 part 2

Read Sec 1.8, continuity

Do Sec 1.8 exercises #3, 7-27 odd, 39-48 all, #54-58 all

NEW Link to Warm-up and flip videos for Math 224 which I will explain in class tomorrow how to navigate.

Wednesday Reminder: All readings and exercises are in Stewart Calculus, 9th ed. e-book on the Cengage site

1. View rest of Limit of a function, started in class, and Detail of limit of sin(x)/x as x --> 0

2. If you are not on solid ground with inequalities and absolute values, read Appendix A in Calculus e-book

3. Read Sec 1.4 and view Tangent and velocity problem

4. Write up to hand in:

Find the instantaneous rate of change (IROC) of f(x) = sq rt x at x = 1. (This is the a value.) Do this by using the detailed formula for finding IROC at x = a and showing all the work that gets you to the numerical answer. It's a limit problem.

Draw an accurate sketch of this function, and indicate with two secant lines arbitrary through the curve at a = 1 and a + h = 1 + h

Write a sentence about the most interesting thing you learned or were reminded of today in class (about mathematics, I mean, though feel free to share other new things you'd like to share)

Friday

Do exercises in Sec 1.4 and do exercises #3, 5, 7 (video and reading in Wednesday homework)

View Derivatives as rates of change

Read Sec 2.1

Do exercises #15, 17, 19, 23, 27

View these important Kazmierczak videos. They are largely review of limits, but without this understanding, the development of derivative has no framework (the first and last I have posted before).

And finally, something we looked at on Friday, but take another look! It will help you soon: Trigonometric limits

First set of WebAssignments, due next week; please do before the due date so you don't miss 8 a.m. posted time:

CLASS WARM-UP: Section 1.4 Monday Oct 31, 8 a.m. (before class)

WEEK 10

CLASS WARM-UP for Section 2.1 Wednesday Nov 2, 8 a.m. (before class)

Monday-Tuesday

Read Sec 2.2 and view the videos therein as well as:

Sec 2.2 Differentiation formulas

Wednesday I moved WebAssign Warmup Sec.2.3 to Saturday night Nov 5; you have Sec 2.4 Warmup on Monday.

Here are Mon and Wed lecture notes from Rui

From p 125 of Sec 2.2, “How can a function fail to be differentiable?” We looked a bit at this. The graph of function fails to be differentiable at points where either we can't establish a tangent line (corners and cusps – think absolute value function at x = 0); at points of discontinuity (kind of obvious); and at a point where the tangent line is vertical, hence its derivative undefined (e.g. cube root function).

Friday: 2-question quiz: something like #15 and #17 (interpreting a graph); something like #27-30 (equation of line tangent to polynomial curve at a given x, use power rule to determine derivative)

To hand in Friday with the quiz: Sec 2.2, #26 use definition of derivative (NO SHORTCUTS–an LCD will be needed)

Continue reading in Calculus, Sec 2.2; do Exercises #3, 7, 11, 13, 15

View these: Position, velocity, acceleration--nice! and Sec 2.3 Power rule

WEEKEND NOV 5-6

See the SKILLS TEST NEWS from the Director, Professor Kazmiercak

Do Sec 2.3 Derivative rule exercises #1-49 every other odd (#1, 5, 9, 13, etc.) #59, 63, 67, 83, 87

* Read App D and Sec 2.4, trigonometry review and trigonometric function derivatives

View Derivatives of trigonometric functions

Next WebAssigns I gave you a bit more time for Sec 2.3 Warmup. Moved the Practice Skills Test 1 to where you can see it in the WA current list.

CLASS WARMUP Sec 2.3 due 11-6-22 Sunday night

CLASS WARMUP Sec 2.4 due 11-7-22 Monday morning

WEEK 11

Monday

WebAssignments: Sec 2.2 due Nov 8 Tuesday night

CLASS WARMUP Sec 2.5 due Nov 9 Wednesday morning

For practice: WebAssign Skills Test 1. We've covered all the material. Have questions to ask in class!

Do Sec 2.4 trig derivatives p 154 #3, 7, 8, 13, 16, 23, 25, 39, 35, 37, 41, 45 (try also #47, 51)

Wednesday

TWO ANNOUNCEMENTS:

NO LIVE LECTURE TODAY, WEDNESDAY. Lecture will be recorded and posted this evening for your required viewing.

Ms Debra Levy at Cengage asks me to have you write to her directly debra.levy@cengage.com, if you have enrollment problems or other technical issue. She fixes things efficiently.

ASSIGNMENT

Thursday

View my recorded lectures:

Nov 10 part 1

Nov 10 part 2

Read (already assigned Monday night) Sec 2.5 and view Chain rule

Do Sec 2.5 chain rule p 162 #1, 3, 5, 9, 16, 18, 21, 34, 37, 45, 53, 51, 67

Friday to Sunday

MIDTERM IS WEDNESDAY! Do the Fall 2016 midterm and have questions ready for Monday. Skip the question on intermediate value theorem. If you have no questions, I will proceed with the lecture on new material, except for…

… Rui's question on trig limits in class. She was referring to lim as x goes to 0 of sin(ax)/bx. Or, sin(ax)/sin(bx). Thanks, Rui, for asking! She does the exercises. Which translates into high test marks, as I draw from them for the exams I write. We'll discuss both these types of limits.

I did prove the chain rule on my video with f(u(x)) notation! WATCH MY 2 RECORDED VIDEOS (required for Wed attendance) and Prof Mosely on chain rule. The real world scenario is motivating!

On Sunday I'll check Panopto for your viewing time and ask a sneaky question to see if you didn't just leave it running and go to the kitchen.

We start implicit differentiation on Monday (not on midterm). Read Sec 2.6 and see Dr Kazmierczak explain Implicit differentiation

WEEK 12

Monday The old exam I posted is actually the Fall 2016. Here it is again as well as solutions. And below it, the Spring 2016 midterm and solutions.

Fall 2016 midterm and Solutions

Spring 2016 midterm and Solutions

Tuesday I reserved the big room down the hall from my office, WH Room 227, for office hours, 1:30-3:30. That was the window I could get, so be sure you come sometime in that window with questions.

Wednesday-Thursday View Implicit differentiation and read Sec 2.6

WebAssign CLASS WARMUP for Section 2.6 due by class time Friday

WebAssign CLASS WARMUP for Section 2.7 due by class time Monday

Weekend homework in text will be posted Friday

Friday-Sunday

Implicit differentiation (ID) lets us find dy/dx even when y cannot be expressed as an explicit function of x (or other relevant IROC, such as a related rate)

View helpful ID video 1 and ID video 2

* Do Sec 2.6 exercises #3, 4 7, 11, 17, 21, 25, 29, 31, 39, 41

In-class quiz on Monday (inspired by above exercises)

Read Sec 2.7 and view motion videos (rates of change in science, and with deeper focus on motion):

Do Sec 2.7 exercises #1, 3, 9, 17, 21

WEBASSIGN CLASS WARMUP Section 2.6 due Sunday night

WEEK 13 THANKSGIVING WEEK

Mon-Fri The following work is not to be ignored over the break!

Read Sec 2.8 Related Rates and view:

Do Exercises #9, 13 (these are practically the same as the sliding ladder problem) and #2 (circle, see last video)

WEBASSIGN CLASS WARMUPS have been extended. PLEASE do them before the time runs out.

Friday-Sunday

Recent lecture notes (mine)

Here 20221209172236112.pdfis a Brief lecture on rates of change in science, but at the start I do an exercise from Stewart on implicit diff'n as well.

The final sections we will cover are Secs. 3.1, 3.3, 3.4, 3.5 (Sec 3.2 is covered in Math 225)

View Finding critical numbers of a function and local max and min

Finding absolute max and min of a fcn on a closed interval

Read Sec 3.1 and try textbook exercises: Sec. 3.1 #1, 3, 9, 11, 17, 18, 31, 35, 41, 45, 51, 59

NOTE: Skills Test 2 begins Nov 28. It covers trigonometric derivatives, chain rule, and implicit differentiation. You have until Dec 9, to take all 3 attempts.

WEEK 14

Monday-Tuesday

Read 3.3

Continue Sec 3.1 exercises.

(I didn’t do absolute extremes today, only local, of which there is more to say about the first derivative test for local maxima and minima, as demonstrated in class today, but not named as such. Much more on this soon.)

Webassign 3.1 warmup due Wed morning

Webassign 3.3 warmup due Wed night

View First derivative add shape of a graph and Second derivative and shape of a graph

Wednesday-Friday

Webassign 3.4 warmup due Friday morning

Do Sec. 3.3 #1, 4, 11-14, 15, 17, 20, 21, 27, 43, 49, 62, 63

My handout summary (used in class today) of Curve sketching with calculus

Today's recorded remote class

Thursday note I was looking at the exercises I mentioned in lecture yesterday, and I meant to assign #18 in obht Sec 2.7 and 2.8. The first #18 is interesting because its derivative is linear, but it will be good to see how it relates to absolute max and min!

Hold off on Sec 3.3 till I decide on two good ones.

Weekend assignment

View How to sketch a curve

In place of Dr Kazmiercazk paper assignment, you are doing this one, to hand in Monday: HW Quiz 5*.

* I forgot to add identify any vertical and horizontal asymptotes. Please do so by using the limit definitions if they apply.

We will use Dr. Kazmaierczak’s for curve sketching review this week.

WEEK 15

Monday

I was looking at Stewart solutions manual, and I notice it has slightly different problems (actually, the same, but different numbering, some of them). They are from an earlier edition. So after my class tonight I will match them up and post pics of many I like including the ones you did.

For homework, be sure you have read through Sec 3.5 (but skip Sec 3.2)

On Wednesday I will go over the Kazmierczak problems (not to hand in) and we will do a selection of Stewart problems on limits at infinity, from Sec 3.4 (no hw on those tonight, but catch up if you need to on WebAssign).

Wednesday-Friday

Sec 3.4 exercises #7, 8, 13, 17/18 (limits at infinity)

Recent notes through Friday part 1 and part 2

Previous exam (2016) with solutions

Derivatives: Flipped Calculus at Binghamton SUNY

2015-08-28T22:35:37-04:00

The Derivative as a Function

Section 2.2 in Stewart's Calculus.

Department of Mathematics and Statistics, Binghamton University

people:mckenzie:math223

Derivatives: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

The Derivative as a Function

Differentiation Formulas

Trigonometric Derivatives

The Chain Rule

Implicit Differentiation

Rates of Change in the Sciences

Related Rates

Laura Anderson and Joseph Brennan

Applications: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

Linearization and Differentials

Critical Points and the Closed Interval Method

The Mean Value Theorem

The Shape of a Graph

Horizontal Asymptotes

Curve Sketching

Optimization

Antiderivatives

Laura Anderson and Joseph Brennan

Integrals: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

Definite Integrals

The Fundamental Theorem of Calculus

Indefinite Integrals

Integration with Substitution

Area

Volume

The Average Value of a Function

Laura Anderson and Joseph Brennan

Limits: Flipped Calculus at Binghamton SUNY

Flipped Calculus 1 at Binghamton

The Limit of a Function

Tangents, Derivatives, and Rates of Change

Limit Laws

Continuity

Laura Anderson and Joseph Brennan

Chapter 2

Calculus Chapter 2

The Derivative as a Function

Differentiation Formulas

Trigonometric Derivatives

The Chain Rule

Implicit Differentiation

Rates of Change in the Sciences

Related Rates

Linearization and Differentials

Chapter 1

Calculus Chapter 1

The Limit of a Function

Tangents, Derivatives, and Rates of Change

Limit Laws

Continuity