9 ====== TODAY!!!! 3/23/2021 DO NOT ZOOM Work on this ===== 8 ====== TODAY!!!! 3/22/2021 DO NOT ZOOM Work on this ===== 7 =========== Very Late Sunday Night /Monday Morning 2/15-16/2021 =========== 6 =========== Late Sunday Night 10:08 PM 2/7/2021 ------------ 5. ========== EDITED: To take a limit: (2/5/2021) ============== 4. ========== To take a limit: (2/1/2021) ===================== 3. ========== 2/1/2021 Announcements ---------- ============== 2. ========= Report on Letters of sp2021 2/1/2021============= 1. letter with zoom urls ============== 12:54 PM 1/2/2021 ====== 00. ==== Spring 2021 Important Dates ======= 1/1/2021 ======== 0. == url for ZOOM meetings/classes schedule, contact info == 1/1/2021 END Table of Contents **************************************************** 9 ====== TODAY!!!! 3/23/2021 DO NOT ZOOM Work on this ===== DO NOT USE THE PINK BOX OR EMAIL TO CONTACT ME. DO NOT SENT ANYTHING TO ME TODAY. Today, you are working alone or with others on: "Day 14 Extreme Values and the Mean-Value Theorem (3.1-3.2)" but you are NOT HAVING A ZOOM MEETING. Here is your assignment. ------------- 3.1 -------------- 1. Define secant, tangent, average rate of change, instantaneous rate of change. * secant, a line which intersects a curve in two points. * tangent, a line which intersects a curve in exactly one two point * average rate of change, average over an interval (from a to b), slope of the secant througn (a f(a) ) and (b, f(b) )containing * instantaneous rate of change. 2. Summarize the vocabulary on page 129. Extreme Values, Relative maximum and minimum values Let f(x) be defined on an interval I containing c. * f(c) is the minimum (also, absolute minimum) of f(x) on I if f(c) ≤ f(x) for all x in I. * f(c) is the maximum (also, absolute maximum) of f(x) on I if f(c) ≥ f(x) for all x in I. * The maximum and minimum values are the extreme values, or extrema, of f(x) on I. * The relative maximum and minimum values comprise the relative extrema of f(x). Extreme Value Theorem If f(x) is continuous on a closed interval, then, f(x) has both a maximum and minimum value on I. 3. Draw Figure 3.1.3 on pg. 131 and label the figure with the vocaculary and items mentioned on pg. 129. 4. Define: a. critical point. b. critical number. c. critical value. 5. Create, draw a non-linear polynomial function with a critical point on it. Use the definitions in no. 4 to do this. 6. State 4a, 4b, 4c for your figure. 7. Summarize/copy the info of page 132. Copy the instructions and answer the questions in Exercises 3.1. Do 1-6, 8, 10, 17, 22, 24. For 10, 17, 22, 24, show work, sketch the graph (yes, use a calculator or the web), compute the derivative, compute the extreme values. ------------- 3.2 -------------- 1. Define both average & instantaneous rates of change in words and with a formula or equation. 2.Using f(x)= x^2 + 1 and the interval [-1, 3] a. graph the curve. b. state f(-1) and f(3) c. draw the secant containing (-1, f(-1) ) and (3, f(3) ) d. compute the slope of the secant e. write the equation of the secant. f. find the value of x when f'(x) = the slope of the secant g. write the equation of the tangent to f(x) at this value of x. h. draw the tangent line 3.Write a summary of page 138 and pg 140. Do exercises 4, 8, 13. See you Thursday. 8 ====== TODAY!!!! 3/22/2021 DO NOT ZOOM Work on this ===== DO NOT USE THE PINK BOX OR EMAIL TO CONTACT ME. DO NOT SENT ANYTHING TO ME TODAY. Today, you are working alone or with others on: "Day 14 Extreme Values and the Mean-Value Theorem (3.1-3.2)" but you are NOT HAVING A ZOOM MEETING. Here is your assignment. ------------- 3.1 -------------- 1. Define secant, tangent, average rate of change, instantaneous rate of change. 2. Summarize the vocabulary on page 129. 3. Draw Figure 3.1.3 on pg. 131 and label the figure with the vocaculary and items mentioned on pg. 129. 4. Define: a. critical point. b. critical number. c. critical value. 5. Create, draw a non-linear polynomial function with a critical point on it. Use the definitions in no. 4 to do this. 6. State 4a, 4b, 4c for your figure. 7. Summarize/copy the info of page 132. Copy the instructions and answer the questions in Exercises 3.1. Do 1-6, 8, 10, 17, 22, 24. For 10, 17, 22, 24, show work, sketch the graph (yes, use a calculator or the web), compute the derivative, compute the extreme values. ------------- 3.2 -------------- 1. Define both average & instantaneous rates of change in words and with a formula or equation. 2.Using f(x)= x^2 + 1 and the interval [-1, 3] a. graph the curve. b. state f(-1) and f(3) c. draw the secant containing (-1, f(-1) ) and (3, f(3) ) d. compute the slope of the secant e. write the equation of the secant. f. find the value of x when f'(x) = the slope of the secant g. write the equation of the tangent to f(x) at this value of x. h. draw the tangent line 3.Write a summary of page 138 and pg 140. Do exercises 4, 8, 13. See you Wednesday. 7 =========== Very Late Sunday Night /Monday Morning 2/15-16/2021 =========== Hi. 1. You already have a print copy of: derivative connect-the-dots at http://www.mathnstuff.com/papers/condots/conpdf/dercondots.pdf We will again use it. 2. Please print: Sing Taking a Derivative - Product, Quotient, and Chain Rules (for Composition of Functions) 3. Please print: Derivatives notes http://www.mathnstuff.com/math/spoken/here/2class/420/derivatives.pdf found at: http://www.mathnstuff.com/math/spoken/here/2class/420/derivatives.htm 4. We will also use: Derivative Calculator at at https://www.derivative-calculator.net/ and Program Your TI84 Calculator to "Take a Derivative at a point or Evaluate a Definite Integral" http://www.mathnstuff.com/math/spoken/here/2class/400/prgm83.htm#calc linked from http://www.mathnstuff.com/math/spoken/here/2class/420/c42pg00.htm 5. Attached are graded papers and your grades. See yah. Hope your weekend was great. a^2 end 7 =========== Very Late Sunday Night /Monday Morning 2/15-16/2021 =========== 6 =========== Late Sunday Night 10:08 PM 2/7/2021 ------------ Hi. I know it is late. 1. I still have not received tests /cheat sheets from some people. 2. Please print for your nrxt class: On "Calc I Notes" at http://www.mathnstuff.com/math/calc/calc1.htm Please "Print just numbers 1 - 3 For the first class of the week. 1. dy/dx Practice1.gif 2. dy/dx Practice2.gif 3. derivative connect-the-dots 3. stay safe. a^2 6 end =========================== 5. ========== EDITED: To take a limit: (2/5/2021) ============== 4. ========== To take a limit: (2/1/2021) ====================== analytically (with a graph) * think "approach" * find the limit from above * find the limit from below * if they are equal, you have the limit * if they are not equal, the limit does not exist * if either is + infinity or - infinity, the limit does not exist * if either oscillates so you can not determine a limit, the limit does not exist numerically (with a table of (x, f(x) ) * use the steps from analytically but using the numbers in the table algebraically (with a familiar function expressed algebraically or with a familiar graph) * consider continuity * use limit to complete taking a derivative by memory (because you need it often and do not need to show work) with tricks and short cuts. "If a function is continuous at c, to take the limit at c, just plug in c in the function and f(c) is the limit." w/a table of limits (because you need it often and do not need to show work) 4. =========END To take a limit: (2/1/2021) ====================== 3. **** 2/1/2021--------- Announcements (for this week) ---------- *** * No Weekly Report on Friday, Feb 5th --You will be turning in TestA1 and your cheat sheet. * No receipt for the cheat sheet -- Your numbers will be posted in class if your cheat sheet has been received. * for cheat sheet, a properly named pdf is best * the assignment code is T1Acheat *1st class of week: finish all (or most) content * between classes do your choice of odd problems completely & check answers * just before class chat about which problems to do * 2nd class of week finish content and go over some hw problems *** Test will be posted Thursday afternoon & removed Friday at midnight **** 2/1/2021--------- End Announcements (for this week) ---------- *** 2. = Report to Students on What They Said in Their Letters of sp2021== 2/1/2021== Perhaps you do not care. I find your replies to my letter both informative and a change factor in how and what I teach. Here are a few things I learned. Stay safe. a^2 ------------- non-academic life ------------ life guard mother military former military visiting, non-matriculated Former Martial Arts Instructor Amateur Artist working engineer ----------------- academic background ---------- many A and B and C students many college graduates seeking a STEM degree many have been away from school for a while some have had calc before many visual learners some have trouble w/textbook ------------ covid experience ------------------- some on whom covid has had no impact one mentioned having strict safety protocol at work some for whom covid has added mental strain and stress some who's loved one(s) have been taken by covid at least one who has covid right now at least one who has recovered from covid some w/lost jobs or cut back hours due to covid at least who had lost a job but now has a full time job plus taking this calc course one get his shot already ----------------------- requests --------------- "You" have asked for * step by step instructions * to do more examples in class * doing practice questions in class * for in depth instruction on the material * to decrease the amount of review before the new calc material * to briefly revisiting the pre-calc before continuing with the calculus In number 13. of the Letter, I wrote, " · If you wish me to go over a problem then perhaps give a list of instructions, this I can probably do. " · If you wish me to go over more problems similar to the first, you will need to come to my office." ONLY 1 person has asked for an office hour. 2. = END Report to Student Letters of sp2021== 2/1/2021== 1. letter with zoom urls ============== 12:54 PM 1/2/2021 ========= Welcome ALL Class! Prof. Agnes (A^2) Azzolino Math Dept., Middlesex CC 1/2/2021 Welcome to the Spring 2021 Semester! This is your math prof, Agnes Azzolino. DO NOT VIEW THESE LINKS IN CANVAS. GO THROUGH AN INTERNET BROWSER. Course info is found in a video at https://www.youtube.com/watch?v=CkzRRzsWvSQ&feature=youtu.be and at http://www.mathnstuff.com/math/math.htm , my semester web page. To contact me use the Pink Box on my semester web page. This page also has links to your course material. All classes are on zoom and since it is remote live you are to attend all classes. Zoom requires you to register before permitting you to enter a class so, go to class early to register. PLEASE VIEW THE ABOVE LINKS BEFORE CLASS. Have a great semester. -- a^2 ------------------ end 2 ------------------------------------------------------ 00. ==== Spring 2021 Important Dates ======= 1/1/2021 ========= Spring 2021 January 1 Holiday --No Classes January 18 Martin Luther King Jr. Day -- No Classes January 19 Spring Convocation; First Day of Faculty Meetings January 20, 21 Change of Program, Advisement by Faculty January 25 Spring Semester -- Classes Begin February 15 Presidents' Day -- No Classes March 13 Spring Recess Begins -- No Classes March 20 Weekend Classes Resume March 22 Regular Classes Resume April 2 -- 4 Holiday -- No Classes May 11 Spring Semester -- Last Day of Classes May 12 -- 14 Specially Scheduled Final Examinations May 19 Last Day of Faculty Obligation May 20 Commencement 0. ==== url for ZOOM meetings/classes schedule, contact info == 1/1/2021 GRADES WILL ONLY BE DISCUSSED IN AN OFFICE HOUR. Appointment required. Contact Prof via the Pink Box at: http://www.mathnstuff.com/math/math.htm -------------------------------------------------- OFFICE HOURS Office.LATE Monday 2:30 - 4:35 https://zoom.us/j/96233475571 Office.EARLY Tuesday 9 - 9:55 am https://zoom.us/j/94869041985 Office. LATE Tuesday 12 - 1:55 pm https://zoom.us/j/92000309383 --------------------------------------------------- Submit attachments/tests/quizzes to: ysp21@mathnstuff.com Submit attachments/tests/quizzes to: gsp21@mathnstuff.com Submit attachments/tests/quizzes to: bsp21@mathnstuff.com ------------------------------------------------- YELLOW CLASSES Y.MAT-131, -090 Monday 8:00 AM - 10:55 https://zoom.us/j/97160350242 Y.MAT-131 Wednesday 8: - 9:50 AM https://zoom.us/j/93378524755 GREEN CLASSES G.MAT-131 Monday 12:00 PM - 2 PM https://zoom.us/j/93915753079 G.MAT-090, 131 Wednesday 11 AM-1:50 PM https://zoom.us/j/96948943337 BLUE CLASSES B.MAT-131 Tuesday 10:00 -11:50 AM https://zoom.us/j/98694439972 B.MAT-090, 131 Thursday 9:00 AM - 12noon https://zoom.us/j/95458532630