Turn in #8 is due Monday, Nov. 17, 2014!
This is for discussing assignments from WEEK 11 & WEEK 12, including homework,
turn-in #8, FINAL EXAM REVIEW & QUESTIONS, and in-class work or lessons, or anything else related to the
class from this week. As this board covers two weeks, the maximum number of points will be 2 bonus points for participation (you must participate more than once to earn both points). Please be sure to include your
name at the end of your post for credit. When answering a question, DO
NOT GIVE SOLUTIONS! Provide hints or explain a method that you used, but
do not give the final result. As always, RESPECT IS A MUST! Anyone
abusing this forum will be banned from future use (meaning, no extra
credit!!!).
For the roller coaster project, does a linear lift ramp count as one of the 5 functions? If so, is it okay that the roller coaster is not differentiable where the horizontal loading area meets the linear lift ramp? Thanks,
ReplyDelete-Safia Sayed
No, the ramp is not one of the functions, and no the curve does not need to be differentiate here (although it probably should be...)
DeleteWill the answers for the final exam review be posted?
ReplyDeleteThanks,
Rachel Hersch
I do not have a key made and cannot promise to do so. If I get one made, I will post it. The review is a guide. Treat them as problems you should be comfortable doing.
DeleteFor the final exam, will we need to know how to show how to get the derivative by the difference quotient?
ReplyDeleteThank you!
Maggie Hammond
Yes, although this topic frequently shows up in the MC section of the AP.
DeleteOn the turn-in for number 3 does g(x) fully level out at a and b?
ReplyDeleteThanks,
Rachel Hersch
g(a)=0, but g(b) is not 0.
DeleteFor the roller coaster project, does a linear function count as a different type of family?
ReplyDeleteThanks,
Lexi Kizy
If parts of the piece wise functions aren't clean fractions is it okay to round to the nearest thousandths place for the roller coaster project.
ReplyDeleteThanks!
Laura Goo
In the world of engineering it is impossible to build to exact specifications, thus we allow tolerances. In this sense, we can allow for our normal AP rounding rules on this project.
DeleteFor the roller-coaster project, can we have the loading track be at the end of the roller-coaster, instead of at the origin and the start of the roller-coaster? I don't think it would matter, because the roller-coaster connects and is continuous, but just checking.
ReplyDeleteThank you!
Maggie Hammond
You can place it wherever you like.
DeleteIs it appropriate to apply L'Hopital's to number 2 on the turn in since you would get an indeterminate value as the limit approaches 1?
ReplyDelete-Kelsey Nowak
Yes. L'Hopital's rule applies to number 2 since the limit would be an indeterminate value.
Delete-Allison Honet
Is the quiz tomorrow a non-calculator quiz or will we have problems similar to those on the back page of the "What does it mean when I evaluate a definite integral" packet? I'm not sure if this was already specified or not, but I wanted to be sure.
ReplyDeleteThank you,
Julia Berthel
Calculators will be allowed. There will be at least one problem requiring use of "fnInt".
DeleteI am a little confused on the challenge FTC sheet from class on Friday for number 4. How do you take the answer to the piece wise function part and get an answer to the integral? Are you supposed to add up the solutions of each part of the piece wise function or do it some other way?
ReplyDeleteThanks,
Emma Gijsbers
You can use G as the anti derivative of f, and evaluate from x=-1 to x=1 directly.
DeleteOn number 4 in the turn-in, how can we use what is given for f to determine the concavity of g?
ReplyDeleteAngela Satullo
You do not need to know the con cavity of g to answer #4. Try drawing a graph of what f may look like and consider g(1), g(2), and g(3).
DeleteFor the roller coaster project, is it okay if there is only one peak if all the other requirements are fulfilled?
ReplyDeleteThanks,
Laura Goo
Yes.
DeleteOn the last page of the "Using the Fundamental Theorems of Calculus" packet, is x=2 considered a relative maximum even though the derivative of f(x) doesn't exist there?
ReplyDeleteThanks,
Rachel Hersch
Does the derivative change signs from + to - there? If so, it's a max! Think about the definition of a critical point.
DeleteFor FTC part 1, when you have variables in both the upper and lower limit, do you always have to split the interval up using 0, or can you use any constant value?
ReplyDeleteThanks,
Laura Goo
You can use any number because it will just be a constant value. Personally, I think that it is easier to just use 0.
Delete-Lexi Kizy
You can use any constant value; we have just been using 0 because it's an easy to evaluate.
Delete-Jenna Weed
On the Using Fundamental Theorems of Calculus worksheet, I'm confused on how to do #4 on the last page. How do you find the slope at a sharp point?
ReplyDelete-Amanda Bachand
to write an equation for a line tangent to the function g at x=4, the slope, m=g'(4). Since g'(x)=f(x), you do no need to find the slope at x=4, just the y value at f(4).
DeleteAngela Satullo
For the FTC worksheet on the fourth page, number 8 asks where h''(x) will fail to exist. I I know the answer is x= 3 and 4 but is this asking where the graph of f is not differentiable?
ReplyDeleteCorrect. Since h'(x)=f(x) by FTC, then h"(x)=f'(x). So, whenever f' fails to exist, h" does not exist.
DeleteAnswers to the Final Exam Review are now posted in the course folder titled "Review Materials".
ReplyDeleteFor the project does a second f(x)=a count as another parent function? Also if you have a sin and a cos graph do those count as two parent functions?
ReplyDeleteNo, on the Handout it says that a horizontal loading ramp doesn't count as your parent function, I would take it that it doesn't count on other parts of the roller coaster.
Delete-Marie Suehrer
Also, on the handout, "trigonometric" is listed as a family, so my guess is that the sine and cosine function count as two functions, but only one type of function.
Delete-Safia Sayed
You can use constant functions as pieces, yes. Sine and cosine are both types of trigonometric functions, as Safia says, so they are not different families of functions.
DeleteWill I get credit for the Coaster thing if I do first, second, third, and fourth order functions? Like are they considered separate families?
ReplyDelete-Julia Trombley
If you mean that you are you using polynomials of various degrees, then yes that is fine.
DeleteFor the coaster project, when I am connecting a sine graph to another graph, the decimals are really long, can I just round to the 3rd decimal place and say that the graphs are continuous there?
ReplyDelete~Katie Weitzel
Yes, use our AP rounding rules. In the "real world" we will not often be able to get something to fit EXACTLY, which is why we allow for tolerances. All of our future engineers will appreciate this some day...
DeleteFor the roller coaster project, is it required to have a starting platform above zero?
ReplyDeleteSarah Fried
No, your loading area can be at any height you choose. Be creative :)
DeleteWhen evaluating the limit of a function and you get a number over zero is there anything you can do?
ReplyDeleteThanks,
Rachel Hersch
A constant divided by zero is undefined. You can write "undefined" or "does not exist". :-)
DeleteWhen using u-substitution, does it matter what you define as u? Can there be multiple correct answers, or are there some substitutions that don't work?
ReplyDelete-Safia Sayed
Typically there is only one choice of u that works (think about the example today with cotx and cscx).
DeleteFor u-substitution, do we decide whether to solve for du or dx based on the specific problem?
ReplyDeleteThanks,
Allison Honet
You are always solving for dx. Du is just something you put in when you use u-substitution because you are changing the variable from x to u. U-substitution is just supposed to be an easier way to solve the integral.
Delete~Katie Weitzel
For u-substitution, I am a little confused on the last part of the definite integrals. Why do we not need to put the function back in for u? Would it be wrong if we did substitute the equation back in?
ReplyDeleteThanks, Emma Gijsbers
For definite integrals, you do not need to put the function back in for u because you found new end values in terms of u. If you did put the function back in for u but used the end values in terms of u, then it would be wrong. I suppose that you could just not change the end values and then replace u with the function at the end, but that takes more time.
Delete~Katie Weitzel
Katie is right, you COULD avoid changing the limits of the definite integral, but then you must substitute your original function back in. I do not advise this method for a couple of reasons. First, it can be cumbersome and opens the possibility for an arithmetic error with the repeated substitutions. Second, sometimes upon changing the integration limits we obtain "nicer" values to use in the anti derivative.
DeleteDo we know how to solve for c yet? If we were given a value of the integral, would we just set that equal to the function and then solve for c? Also, is there a way to solve indefinite integrals on a graphing calculator?
ReplyDelete~Katie Weitzel
No, we haven't explicitly shown how to solve for C. The last few problems of today's in class wkst are to get you thinking in that direction. And no, you cannot solve or graph an indefinite integral on the calculator because it is indefinite (there are infinite solutions, all varying by a constant).
DeleteDoes our roller coaster have to be differentiable at the points connecting the loading area to our first and last functions?
ReplyDelete-Amanda Bachand
No, I heard that it doesn't have to be differentiable there.
Delete-Rafey Rehman
It should be differentiable there, but I will not mark down for it. I should note, however, that to be differentiable a function must also be continuous. You must show this.
DeleteHey, Mr. Wilson
ReplyDeleteIf I dont have much room under some of my curves to write out the proof of each equation, could i do the math on a seperate sheet and staple it on?
-Will Schwartz
That is fine. You could also write it on the inside of the folded poster.
DeleteThanks. I think I'm going to do it on a separate sheet
DeleteSuppose I solve a definite integral on a calculator with respect to x. For some odd reason, I decide to solve it by hand as well. On paper, I use the u substitution method and solve the integral with respect to u. Will my answers be the same or will they vary because they were solved with respect to different variables?
ReplyDeleteRafey Rehman
The will be equal (or approximately equal since you may get an approximate result from the calculator) as long as you correctly changed the limits of the definite integral.
DeleteWhat's the difference between speed and velocity?
ReplyDeleteThanks,
Rachel Hersch
Speed is the absolute value of velocity. Velocity has a direction associated with it (positive for right/up, negative for left/down), speed is just a magnitude ("the car drove 50 mph" as opposed to "the car drove 50mph westward").
DeleteWe will be given the formulas for weird or difficult shapes for related rates problems, right? Just like before?
ReplyDeleteThanks,
Julia Berthel
Well, if you're classifying a cone or sphere "weird", then yes. :) Most volume formulas are provided on the AP. You should know area formulas for triangles, rectangles, trapezoids, circles, etc.
DeleteWith our term 1 final exam to begin tomorrow, here's a list of topics that come to mind. I may have missed something, but you SHOULD be familiar & comfortable with each topic below (especially #2!).
ReplyDelete1. Limits & continuity (the building blocks of calculus!): IVT
2. Derivative rules: power rule, trig and inverse trig, exponential with bases other than e, logarithms with bases other than e, product rule, quotient rule, CHAIN RULE.
3. Derivative techniques: implicit, logarithmic
4. Derivative applications: optimization, related rates, curve analysis (concavity, POI, etc.), L'Hopital's, MVT
5. Areas under curves & Riemann sums: LRAM, MRAM, RRAM, trapezoids
6. Integration: definite & indefinite integrals, FTC
7. Integration techniques: anti-derivatives of known functions, power rule, substitution
Good luck! Go Falcons!
This board is now closed for points. I will open a new board for Week 1 of term 2 after Thanksgiving. Enjoy the much-needed (and well-deserved) break this weekend!
ReplyDelete