The question was to find the lines tangent and normal to the given curve at the point (-1,0). You need to differentiate implicitly and then solve for y’ (aka dy/dx). The top image is the solutions manual version and the bottom image is my solution. Both yield the same result, but the first uses dy/dx notation whereas I used y’. Sometimes the notation makes it very confusing! I get it.
Here are a few important links:
Solutions Manual (you will need to use the password I gave you to access the content): https://www.danjonesmathematics.net/homework-solutions/
Go to the HOME PAGE and look at the resources including help videos and pages created by section under the AP Calculus BC menu tab.[/fusion_text][/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]
I looking forward to seeing you all tomorrow! Please bring your school ID as I will be checking out books tomorrow night…..
Homework: Yes there is homework for the next 3 days, but you choose what you need practice on and what you don’t. This will change when school actually starts. All you need tomorrow is a working brain and something to write with, I will have a packet for you! If you are unsure about the working brain thing, you have about 24 hours to find it and make it work again!
I have subscribed you all to the course calendar (google) and it should now appear in your calendar. It is also viewable on my website at: https://www.danjonesmathematics.net/bc-calculus-calendar/
I also have Purple and Gold Google calendars (that are used by more than 100 staff at RMHS), if you would like to be added please shoot me an email at [email protected]
Ah that message you were either excited about or dreading! PLEASE READ ALL!
When: Monday, August 5th – Thursday August 8th 5:00-6:30 (we will probably be done on Wednesday night! Please note that I have changed the time to accommodate band conflict)
Where: RMHS South Cafeteria (this is tentative as I am still waiting on confirmation).
What if: If you can not attend on a particular night, I will post notes each day on my site…..I will provide that link on August 5th – my next post.
What to Bring: ID (I will check out books – no ID, no book), I will have packets for you, something to write with and YOUR BRAIN!
What now: Relax enjoy the rest of your summer!
You all have worked so very hard and learned so much this year – I am truly proud of all of you! I know you will all do your best tomorrow and you will put in your best efforts, just like you have all year – why would tomorrow be any different? You are as prepared as you are going to be!
Make each part or each question a celebration. Start with an empty glass and fill it up! – don’t think about what you might have missed, celebrate what you know, and fill up the glass to overflowing. Your glass is your goal. I believe that all of you can and will reach the goal that you have set.
The quote above is from Dr. Suess’ “Oh the Places You Will Go!” – one of my favorite books! For the full reading of the book approx 6 min, the video is below.
I will stop down just before the exam! The best of luck to all of you!
HERE is a link to the notes from Today if you were absent! Please Read
Here are a few links to Khan Academy for videos and even some practice MC Questions for polar and Integral as a limit of a Reimann Sum!
Integral as a limit of a Reimann Sum Video: https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/writing-riemann-sum-limit-as-definite-integral
Integral as a limit of a Reimann Sum Practice: https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/e/the-definite-integral-as-the-limit-of-a-riemann-sum
Area between 2 Polar Curves Video: https://www.khanacademy.org/math/ap-calculus-bc/bc-advanced-functions-new/bc-9-9/v/area-defined-by-two-polar-graphs
Area between 2 Polar Curves Practice: https://www.khanacademy.org/math/ap-calculus-bc/bc-advanced-functions-new/bc-9-9/e/area-between-two-polar-curves
This was missing from the calendar….this is the assignment that is due tomorrow:
11.1 Parametrics HW p. 541 # 7,11,23,25,27,33, 47,48,50 11.2 Vectors p.552 #21,29,31,40,42,55,56
It is also on the calendar
Remember to partner up with 3 or 4 of your classmates and bring a Pie for class tomorrow. I will NOT be able to store it for you during the day so please plan accordingly. I will have plates, napkins, forks and serving utensils. See you tomorrow!
I realize that there are still a few weeks, but only a few of you have signed up so far – I am expecting that all of you take an AP Calculus Exam – whether that it is the AB or the BC Exam.
Have a great weekend!
Chapter 9 Tests are posted…..bring 10.1 HW tomorrow. Since last weekend was a (cough, cough) no homework weekend (you got enough of them with the snow days!), I will count the 1st 10.1 as extra credit.
So you must have completed the assignment from 2/19/2019 to get the extra credit for the 2/14/2019 assignment. See below.
We made it to Chapter 10! We will spend about 15-20 minutes with Geometric series and start 10.1, then the remainder of class will be the Chapter 9 test/Quest.
I looked at the packet we started last class and I want to change a few things, so I will have a new one for you today. In addition, I did update the retakes scores from last Friday. All of you either stayed the same or did better and the questions were a little harder.
See you soon!
Sooooo, we need work on limits, continuity and differentiability We will go over them tomorrow in class and we will do a retake on Friday at the end of the period or after class. I will replace the grade.
Here is everything for Sequences and L’Hôpital’s (Also written L’Hôspital’s) Rule for finding indeterminate limits. Please note that L’Hôpital’s is extremely important for “laying groundwork” for Chapter 10 on Series and convergence which is often one of, if not, the most difficult Chapter for students. Please make sure you spend the time to understand it.
- Blank Notes Page for those of you who like to write your own notes.
- Completed Notes Page to accompany video.
- I broke it down into 4 videos….each one gets shorter!
1. AP problems are due on Monday when we return AND we will have the Chapter 8 Test on Monday also, so please use your time wisely over the next 6 days and stay warm and safe!
2. Obviously with the incoming cold weather we need to make some adjustments to the schedule – which I already have completed on the class calendar. Missing 1 day is not too much of a problem, but missing 2 creates some problems with time during AP Review time, since the AP Exam date is fixed. How can we time travel and make up time? I am going to create a few video(s) for the 2nd Day of Chapter 9.1 on Sequences (we started at the end of last class) and the start of 9.2 on L’Hopital’s Rule – which is extremely important. I will send you a copy of the completed notes page to accompany the video(s). This will help “recover” one of the days. My expectation is that you will watch and learn from the video(s). There will also be an assignment that relates to the video which will be due on Wednesday of next week (after the test)……so you can watch the videos anytime, but the assignment will be due on Wednesday, February 6th. If you look at the calendar, it already reflects these changes. You may need to move forward on the calendar to see the month of February. Calendar.
3. I should have the video(s) and notes completed and posted for you by Friday along with the assignment – which is already on the calendar.
Hopefully we will all be able to manage all of this. Hopefully your AP problems are almost complete and you are in pretty good shape for the chapter test.
Stay Warm (or try to) and have safe few days off! please email me if you have any questions.
There will be a non-calculator part of the test. Topic: Limits (limits at a point and limits as we approach +/- infinity), continuity and differentiability.