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[WSG20] Calculus Daily Study Group begins August 3 (Free!)

Posted 1 year ago
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The latest Wolfram Daily Study Group features one of our favorite math instructors, Devendra Kapadia, and focuses on building fundamental concepts in calculus. This is a great opportunity for students to refresh their knowledge or get a head start on the subject. Sign up:

113 Replies

@Devendra Kapadia

Dear Devendra,

Thank you for your expidited response. Do you mind if I ask you to do one more double check? This time, there is no marker (options to choose the correct answer) in front of the multiple choice in the question number 3 in Quiz 10. Thank you. Best wishes,

@Chloe Allen, there are three different Wolfram U certifications available related to calculus! 1) To earn a certificate of program completion for the Study Group, you need to have registered for the Study Group, attended the sessions or watched the videos, and pass the three quizzes. 2) To earn a certificate of course completion for Introduction to Calculus, you must watch the course videos and pass the course quizzes. 3) To earn a Level I certificate in calculus, you must complete the interactive course and pass the final exam. The latter two certificates can be monitored using "Track my Progress" from within the course.

Both these issues with Quiz 10 in the online Calculus course have been fixed.

You will need to delete the copied notebooks, both in your 'Copied Files' folder and then in your Cloud 'Trash' folder to see the changes.

Thank you for bringing these issues to our attention, and sorry for the inconvenience.

You are indeed correct about Q2 (the correct answer is 1.108) and the typo in Q5., We will fix these errors soon. Thanks!

@Abrita Chakravarty

Thanks for this update. I completed the Quiz 10 just before, and I want you to do the double check for the following two questions:

The question 2: I think the correct answer is 1.108 (rounded from 1.10763); The question 5: There is a TYPO in the first choice ("A." is inserted).

Please see the attached as well.



Hi Joseph, Yes we are putting these together for you and will send out a link in the follow-up email along with all the other resources from the final week of the study group.

Hi Veronica, we will have the recordings available shortly. Meanwhile you can also take a look at the lecture videos in the online course Introduction to Calculus.

Quiz 10 from Introduction to Calculus course has been re-deployed. You should be able to access it and take it now. Let us know if you continue to face issues.

In some cases you may have to take the following steps to ensure the latest version is loading in your course:

  • Clear out the browser cache
  • Go to My Files -> Copied Files on your Wolfram Cloud account and delete any copies of Quiz 10
  • Go to My Files -> Trash on your Wolfram Cloud account and delete any copies of Quiz 10
  • Close and reopen browser
Posted 1 year ago

Its not fixed yet it seems to me

Is it possible to get the remaining notebooks and Lessons from the Intro to Calculus course that were not provided during the Study Group. One of the surveys towards the end of the study group sesssions asked if there was interest in obtaining these notebooks.The study group was excellent and I would like to finish the online course. Thanks again for a great Study Group and all of them offered this year!

Hello there! I am trying to catch up on the course. I wasn't able to attend some of the days. I've been watching the recordings on but it's missing Days 13 to 15. Will these be uploaded soon for us to catch up before taking the last quiz?

Thanks so much!

Posted 1 year ago

Hi I have really enjoyed the course and have been watching it live (with a few sessions I missed and caught up with).

I am a little confused with quiz and the certification process. Do you only need to complete the 3 quizzes (as in email) to gain the certification or do the 3 quizzes AND watch the 50 course videos, complete the 10 quizzes and the final exam as on ? Thank you.

Cool beans!!!!! Looking forward to it!

We are redeploying Quiz 10. It should resolve the issue. I'll post when its ready.

Meanwhile, for those who have not been able to view the updated Quiz 8, one more thing to try: In addition to deleting the copy of 08_quiz.nb from your "Copied Files" directory in your "Cloud Files"/"My Files" directory, please delete any existing copy of the file you may find in "Trash" as well.

@Abrita, any update on this issue? I am still waiting to complete the course. Best

Hi Lori and Hee-Young, thanks for bringing the issue to our notice. We are working on it.

Dear @Abrita, I am still unable to access and mark the Quiz 10 questions. Thanks.

Hi, Hee-Young Shin! Hi, Abrita! Hi, Devendra!

I am having the same issue in Firefox, so I tried Chrome. There is a tiny horizontal progress bar above the scratch area and the quiz. The scratch area does seem to complete loading but the quiz never does in either browser. My current refresh has been loading for the last ten minutes. Safari takes you to the Wolfram home page when the link to the calculus class is clicked or pasted, so there is no point discussing that.

(30 minutes later) CHROME MESSAGE: "Connection Lost Unable to connect to

You may want to check your internet connection."

There's nothing wrong with my connection because I'm streaming "Ms. Marple" right now, LOL!

I did what Abrita suggested earlier: cleared the cache, deleted quiz 10, restarted the browser. Still no success. Hope this information can help get to a resolution OR maybe it will just work later today :D.

Let me try again after a while and see whether it would work. Thanks.

Hi Hee-Young, I just tested the quiz. The interactivity seems to be working ok i.e. I am able to select the answers by clicking on the radio-buttons. Note, you may sometimes have to wait a bit to allow the notebook to load completely and become interactive. Initially a non-interactive version of the notebook is displayed.

Dear @Devendra and @Abrita,

Here is another call. For some reason, the Quiz 10 (in Introduction to Calculus) does not allow me to click (mark on) the answer among the multiple choice. I suspect that is something to do with 'interactivity' funtionality issue (Not internet connection issue on my part, but something in the program that prevents a user (like me) from choosing a correct answer). Could you please quickly check? (Cf. See also the attached work).

Posted 1 year ago

Devendra, There is a typo in the answers provided for the 9th question in quiz 3.See 3rd multiple choice answer from the top. Best Regards, Rajeev


You are correct. There is an error in the multiple-choice answer to this question (#5 in Quiz 8 (in Introduction to Calculus)). We will have this fixed soon. Thanks.

Dear @Devendra and @Abrita,

I think the question #5 in Quiz 8 (in Introduction to Calculs) does not have a correct answer (in the multiple choice). Could you please quickly check? (Cf. See the attached.)


Hi Joseph,

They represent the roots of a polynomial. Check the documentation for details. If you are just interested in the numeric values then

sol = Solve[f'[x] == 0, x]
(* {{x -> 0.}, {x -> -3.23319}, {x -> -0.422973}, {x -> 3.65617}} *)

It stands for the Root symbol.


represents the exact kth root of the polynomial equation f[x]==0.

This was updated in version 12 and more info can be found here

The second root from your solution looks like this in InputForm

Root[-5 - 12 # + #^3& , 1, 0] 

You can get the corresponding numeric value with:

Root[-5 - 12*#1 + #1^3 & , 1, 0]//N

Great! Thanks for including the third step of "Closing and re-opening the browser". We'll share it with other users facing similar issues.

It is now working for me, @Abrita. Thank you.

For your reference: It turned out that I needed to close and reopen the browser. Therefore, 1. Clear out the browser cache; 2. Go to Wolfram Cloud -> My Files -> Home -> Copied Files and delete any copies of Quiz 7 and Quiz 8; 3. Close the browser completely and reopen it.

notation question

I have encountered an odd square root symbol in the results of a Solve statement as shown in the attached. Can anyone explain this for me?

Thank you, Abrita, for your answer!

Hi Hee-Young, Would you try a couple of things and see if it helps?

  • Clear out the browser cache
  • Go to My Files -> Copied Files on your Wolfram Cloud account and delete any copies of Quiz 7 and Quiz 8

Please feel free to let us know if these steps do not help.

Thank you.

Hi Valeriu, Your final exam submission has been received. We have also received your feedback on the course. The "Certification" system is a new roll out and we are still working on smoothing out the last wrinkles. We hope to reach out to you shortly with your certificate. Thank you.

Dear @Abrita,

I quickly checked, but for some reason the problem still persists:

  1. Both Quiz 7 and 8 are the same as before, with the answer to the Quiz 8 are wrongly indicated.
  2. The answers to both question #2 and #3 in the Quiz 7 are not accurate.

Best wishes,

Hello Everyone,

The following issues have been resolved for the online course Introduction to Calculus:

  • Quiz 4 Problem 4
  • Quiz 5 Problem 2
  • Quiz 7 Problem 2
  • Quiz 7 Problem 3
  • Quiz 8

In addition, a minor correction has been made to the text of Problem 7 in Quiz 2 released last week for the Calculus Study Group.

My calculation with help of the Wolfram Cloud App on my iPad. Same result as Maple solution.

enter image description here

I completely agree with your reasoning and conclusion. I tell my students: if you catch my mistakes, it means that you're paying attention! It applies to us, too :D

In the "Introduction to Calculus" online course, Quiz 7 is the same as Quiz 8. And now, I'm catching up on other posts and see that this issue has been mentioned. Feel free to ignore.

One thing IS certain: one feels much less crazy when the developers have trouble getting code the give the desired results.

Hi Lori,

Thank you so much for support. I have selected the "correct" answer in the quiz, but I do not believe it is correct.


  1. Mathematica calculates the "correct" answer according to the quiz.

  2. If you take the "correct" result and you try to draw a parallel line of the secant through the calculated point, it becomes obvious there is a mistake.

  3. I have done the calculation with Maple as well (sorry Wolfram Team).

Here are the results which look correct and logical to me:

Tools >> Tutors >> Calculus >> Single Variable >> Mean Value Theorem Tutor Math App

My worksheet Part 1 Part 1 of my worksheet

My worksheet Part 2 Part 2 of my worksheet

Hello, Juergen!

It's not you. I got a different and the correct answer, also, using Mathematica of course. These WSGs are very popular and since I got a passing score I didn't report it. BUT, QUIZ 8 of the online course just blew up and now only 2 of my answers are correct whereas YESTERDAY I had only missed one: none of the choices on #2 are accepted but one of the IS the correct answer.

How far have you pregressed?

Posted 1 year ago

Yes off course, forgot, its Lesson 20 Exercise 3 page 8/9

Dear Devendra,

I have completed the online course, i.e., I have watched all 50 course videos, passed all 10 quizzes with a score of 100%, and passed the course exam with a score of 88%. I have reported the developer team for some issues, too. Unfortunately, I haven't received any feedback: no completion certificate, no Level 1 Certificate in Calculus, no any reaction from the Wolfram team for a couple of days. Is the developer team on vacation?

Hi Darko, Could you please point to the transcript notebook, problem session or quiz notebook you are referring to in the issue reported above? Thank you.

Thank you for your feedback on the various quiz questions. We are working on addressing the issues.

We will try to make these available when we send out the updated download link for this week - along with the Q&A and example notebooks.

Hello, The issue with Quiz 8 has been reported to the developer for fixing urgently. Sorry for the confusion. I will also look at the other feedback comments sent by you. Thank you.

Dear Devendra and Jamie,

I have been working on the Introduction to Calculus (, while taking this daily study group.

I have personally sent to you a number of comments (through the "Feedback" menu) regarding the Wolfram U calculus course including what I think some errors and/or incorrect answers in the Exercises and Quizzes.

For example, most questions in Quiz 8 are repetitions from the previous Quiz (rather than asking to calculate the area or volume of solids), and the question number 2, 3 and 5 do not have an accuract answer.

Could you please quickly check these comments that I sent to you (Please see the attached as well)?


Hi Abrita,

Yes, please. I would like to have those stand-alone notebooks for units that we do not discuss in the daily study Group. I prefer to add some notes and to extract the online content by copy and paste cost a lot of extra time.

Hi Juergen, The entire course (containing all the lecture videos as well as transcript and full text notebooks) is available online at Are you requesting stand-alone notebooks containing the "Full Text" for each lecture?

Hi Jamie,

Is it possible to get also all notebooks of the original online course that we do not discuss in daily study group?

Juergen is correct. The quiz I referred to is in the online collection of course materials. Sorry for creating confusion!


I have a problem with the result interval of Problem 2, Quiz 5, Online Course. The task is as follows: enter image description here

In my opinion none of the given answers are correct. According to my calculations the result must be c = 1.527525232. Please check.

Posted 1 year ago

Exercise 3 Slant, Lesson 20

I think there is mistake in putting local minima and maxima(-3,23, 3.66) instead of critical numbers -2, 2 where f' is not defined

Posted 1 year ago

Thanks for clarification yes I am confused too LOL

I have found a link to the Daily Study Group Quiz 2 here: , but the link is not offically deployed. Therefore, I do not know whether it is correct.

We face now a mix up of quizes. Joseph Smith refers to a quiz problem in the original online course You and me are waiting for quiz 2 of the daily study group.

Posted 1 year ago

Quiz 4?? I didnt yet get even quiz 2

I believe there is an error in the above list of answers for Quiz 4 Problem 4. The program accepts 5/18 as the correct answer , but as shown below, I think that the correct answer is 5/(18*[Pi]). The attche notebook provides the details.

Wow Heidi, so beautiful!

Beautiful notes and a beautiful thought!


Posted 1 year ago

This course has a special value for me: I kept my mother's calculus notes. I've had her binder since I was little and wondered about all the symbols and numbers. These pages are about today's lesson. Now, I can look at her notes and understand them better. She was born in 1920. Page 19 Page21

Your advice was great, Jamie, it's working now!!! Thank you very much.

This sounds like a known issue related to Safari cross-site tracking. Please try in a different browser, such as Firefox or Chrome. Your other options would be to turn off cross-site tracking in Safari or add and to your list of website exceptions for allowing tracking.

Hi @Josep Branchat , the link to Week 2 notebooks is being shared during today's Study Group and will be added to the reminder email effective tomorrow. Regarding the interactive course, you will be asked to sign in using your Wolfram ID or to create one. This will allow you to work with the cloud content for this course. If this process is not working for you, please send a screenshot and details to Thank you!

Thank you, Jamie, for your info about the link to Week 2 notebooks!!!

Along with my participation in this study group, I’d like to work through the online course. So I follow the link:

but there is no way I can access the Wolfram U interactive course "Introduction to Calculus" because I am redirected to

Any hint?

@Rohit Namjoshi, the link to Week 2 notebooks is being shared in today's Study Group session (starting in 5 minutes!) and will be added to the email reminder effective tomorrow.

Hi Abrita,

The reminder email I received for todays session has the following

Lecture, exercise and Q&A notebooks:

That link goes to the notebooks and exercises for week 1. Where are the notebooks and exercises for week 2?

Hello, You will find the download link for the lesson notebooks in the reminder email that goes out an hour before the Study Group webinar starts (at 11:00 AM CDT). The email should have the subject "Reminder: Daily Study Group" and is sent by Wolfram Virtual Events. Hope this helps.

Hi @Abrita Chakravarty ! Thanks for checking on me! I am new to the wolfram language, so I couldn't see any kind of "run" command. Then, when I saw in the Mathematica program itself that it's enter+shift, I experimented and figured it out! Took me a few days of struggles! But I can do it now! Thank you! :-) I hope others know now that it's enter+shift, too. :-)

I have the same question: when those notebooks will be available?

Another issue: I try to enter "FULL INTERACTIVE COURSE Introduction to Calculus" but no way. Any hint?

Thank you in advance!!!

The curly bracket is a representation of the Piecewise function. This code can also be written as Plot[{Piecewise[{{x^3 + x, x < 2}}], Piecewise[{{(13*x^2)/4 - 3, x >= 2}}]}, {x, 1, 3}]

Formula with odd-looking curly bracket

The attached notebook and image shows a Plot statement from the solution to problemset 2 problem 2. Can anyone identify the odd curly bracket just before x^3 and before 13x^2/4?

Sorry, I have made a mistake. Everything is ok.

Hi Wolfram U Team,

in parallel I run the quizes of the online course "Introduction to Calculus" Please check Quiz 3. It seems to me the file is corrupted.

Posted 1 year ago

I can't find the Lesson Notebooks for this week? Can you send me the link, please

Hi @Veronica Frans, Were you able to use the scratch notebooks after all? You should be able to click inside them, type in Wolfram Language code, and click Shift+Enter to evaluate the code. If you are unable to do so - let us know what browser you are using.

Thanks to everyone for your attention to Quiz 1 of this Study Group. Each quiz covers topics that were covered the previous week during Study Group. Check your reminder emails for links to the quizzes and other links to Study Group recordings and notebooks. We will not be reviewing the quizzes as a group.

To further clarify, there will be a total of three weekly quizzes. You must pass all three quizzes with a score of 60% or better to earn a certificate of program completion. All scores are recorded, and your best scores will be counted. Quizzes are due by August 28.

Posted 1 year ago

Thanks was wondering what's going on lol

I hope it's not due by midnight.... I was planning to take the quiz in the morning... Yikes! Also, is it timed? Best wishes to all who are taking it!

Is there a specific due date to this? It just has to be done by tomorrow, right? Will we go over this? We are allowed to retake right? If we retake, is it still that the initial score on the first trial is the one that is recorded? For example, I took it the first time and I got a 70% but I realized my mistakes and selected different answers and earned a 100%. Which score will be recorded in order to be eligible for the course completion?

Posted 1 year ago

It was sent on the Friday reminder email.

Quiz 1:

Where can I find the link to Quiz 1? Can anyone tell me?

Posted 1 year ago

Will there be a short overview of the Quiz for Week 1?

I am missing a graph plot in slide 10 of "7DerivativesandRatesofChange.nb". It is stated: "Plot the function, its derivative and the tangent line". In my opinion the plot doesn't show the derivative. I have made the following improvement and would like to get feedback whether it is correct. enter image description here

Where can I get the copy of Quiz 1? I didn’t get it.

Properly formatted

Given that

Limit[f[x], x -> 0, Direction -> 1] = a


Limit[f[x], x -> 0, Direction -> -1] = b

what is the value of

Limit[f[x], x -> 0]

Thank you for bringing that to our attention @Dave M ! We will fix this and redeploy the quiz ASAP.

Question 5 should read: Given that Limit[f[x],x->0,Direction->1] = a and Limit[f[x],x->0,Direction->-1] >> = b, what is the value of Limit[f[x],x->0]?

Posted 1 year ago

FYI, there seems to be an issue with the WSG Calculus week 1 quiz (at least with my copy)...

The wording for question 5 seems to be incorrect (it is the same as for question 6).

Posted 1 year ago

Hi Veronica,

I believe the user has to be signed in into the Cloud for the Scratchbook space to work (?).

I decided to open a second window next to the browser and work the exercises in Mathematica. I need to take my time to type in instead of copy/paste (that did not work for me), it helps me to practice the syntax of the language. I also have a few tabs open at the Documentation Center to look up entries that I do not know about, or not understand, or to alter how graphs render for example.

I am also curious about how others approach the examples and the practice exercises.

I hope this helps. Be well!

Hi everyone.

How are you doing the practice exercises? I don't understand how to use the practice notebook below the videos when I go to the online course. I'm not able to run anything to see the results in there.

Is it possible to receive notebooks of the exercises, similar to how we received copies of the lesson notebooks, so we can work with them in the Mathematica program itself? I just keep struggling going back and forth to try them...

Thanks in advance for your help.

Hi Heidi,

You can always quit the kernel by evaluating Quit[].

Posted 1 year ago

No luck. I ended up opening a new notebook, setting the default context to Unique, from Evaluation in the Menu Bar. This also allowed me to reset my inputs numeration to 1 and retyped as needed. Is there a way to do that (reset the input numbering) within the same notebook? Thank you!

Hi Heidi,

I am unable to reproduce the problem. Are you sure you do not have multiple downvalues for f? Try ClearAll@f.

f[x_] := (x^3 - x^2 + 2)/(5 x - 3)
{Limit[f[x], x -> -2], f[-2]}

(* {10/13, 10/13} *)
Posted 1 year ago

I hope the pictures show as attachments.



Posted 1 year ago

I am having difficulty with an exercise. I do copy/paste to the scratch notebook, and separately to Mathematica and do not see the expected result. Thank you. (apparently I can only add one picture)

Thank you for the feedback. I am glad that you are enjoying the course, and I agree that practice is important for mastering the subject.

Posted 1 year ago

I am enjoying the conceptual approach to the course. Also, the use of "multiple representations" where the connections between a situation, code, table and graph are made. Familiarity with the basics of the language can be a tad challenging, however, learning by example is helpful, in addition to introducing options to the examples and to see how things change. I try to follow with a notebook where I can make annotations and work examples at my own pace. My mother used to say that "Mathematics are learned with a pencil" (not an exact translation, but it gets the message across: practice is important.)

Hello I'm Jonathan

I'm looking to do this to get an idea of how best to help my students.

Thank you, Jamie!

I am looking forward to meeting students and learners from all over the world in the study group.

My goal is to provide an easy introduction to AP, high school, or college calculus.

See you all there!

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