Turn in #5 is due Monday, Oct. 13, 2014!
This is for discussing assignments from WEEK 6, including homework,
turn-in, and in-class work or lessons, or anything else related to the
class from this week. Please be sure to include your
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NOT GIVE SOLUTIONS! Provide hints or explain a method that you used, but
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credit!!!).
For #4 on the in class ws, do you distribute cos(2y-e^3x) in order to eventually get dy/dx alone?
ReplyDeleteYes, distribution is the best way to isolate dy/dx.
ReplyDeleteAngela Satullo
On the turn in for number 1A, would you find the normal line and see where the two equations intersect? Or are there possibly other methods?
ReplyDeleteKelsey Nowak
We are not concerned with the normal line. We wish to minimize a distance between two functions. We know (or will tomorrow) that extrema occur at critical points, so I suggest finding a DISTANCE function (hint, hint) and looking for its critical points.
DeleteIs it acceptable to stop at lim u->0 (sinu)/u = 1 in a problem?
ReplyDeleteThanks,
Rachel Hersch
Yes, I think that works because it is an identity that is well known throughout the calculus world.
ReplyDeleteRafey Rehman
For problem 1b on the turn-in which way is the car going?
ReplyDeleteThanks,
Rachel Hersch
dx/dt is positive pi, so I think it's going to the right.
Delete-Safia Sayed
For the test tomorrow can we use a calculator?
ReplyDeleteThanks,
Lexi Kizy
No.
DeleteDo you apply ln to both sides if there is a variable in the base or if there is a constant in the base?
ReplyDeleteThanks,
Emma Gijsbers
Apply ln to both sides if there is a variable in the base and a variable in the exponent.
Delete-Amanda Bachand
When using L'Hopital's rule, do we need to have the function we are taking the limit of equal to (0/0) or (infinity/infinity) all the time? I'm wondering what we do when the function is just undefined but doesn't equal one of those ratios.
ReplyDeleteThanks,
Amira Kamoo
See your examples sheet from Monday. We have several tricks for getting a 0/0 indeterminant form.
DeleteFor the quiz tomorrow, do we only have to know the derivatives of arcsin, arccos, and arctan out of all the arc trig functions?
ReplyDeleteThanks,
Allison Honet
I believe so. Mr. Wilson circled only those three and said to memorize them; he said the other three are rarely used and shouldn't show up on the AP test either.
Delete-Jenna Weed
i think you should know arccot, but if you know arctan it is just the negative of that
DeleteHow do you find dy/dt for 4a on the turn in?
ReplyDelete-Abby Siegal
I actually meant 4d not 4a
Deletecan you set up a proportion for the distance qr/qp equals dx/dt over dy/dt???
Deleteor can you use a previous answer?
DeleteJulia Trombley
4d is using the same x coordinate as 4c, so you will need that answer for this part. Try to find the area of the triangle in terms of xp and k only, then use the relationships between xp and k from part b and dx/dt, dk/dt from part c.
DeleteFor #4b on the turn in, should we set the equation equal to k?
ReplyDeleteSarah fried
you write an equation using the equation you got for dy/dx as the slope and the point (k,0). Then you substitute in 1/xp^2 for y and solve for k.
DeleteIn part a you will write a point slope equation of the tangent line at x=3, then we know this line passes through (k,0), so we can substitute and solve for k. In part b you are doing the same thing, except x=xp now.
DeleteFor problem 4b on the turn-in, do we put 0 in for y when solving for k?
ReplyDeleteThanks!
Allison Honet
This line passes through the point (k,0), so yes.
DeleteIs there a way to find critical points by looking at the second derivative or is it only useful in telling us if the function in increasing/decreasing and the point of inflection?
ReplyDeleteKelsey Nowak
Critical points are only found by the first derivative. We then can use the second derivative to determine if a critical point is a min or max (concavity of f at the critical point).
DeleteFor 4a on the turn-in, would you set the derivative of 1/x^2 equal to (y2-y1) / ((x2-x1) and put in point P as one of the points? Is this even the right approach to the problem?
ReplyDeleteThanks,
Julia Berthel
For 3 on the turn-in, I found the derivative of a(t) and used that to find the critical points, which I thought would give me the extrema on a(t). However, the value I got for a was lower than some of the values you could get just by plugging in values of t between 0 and 3. Am I overthinking this problem? Can we just plug in 3 to get maximum acceleration?
ReplyDeleteThanks,
Safia Sayed
After finding the critical point, plug in 0, the number you got for the C.P. and 3 into the initial equation. You will get three different values and find the maximum from there. You are on the right track!
Delete-Allison Honet
You want the maximum value for a(t), so you need to find the critical point of a(t) using a'(t).
DeleteI'm a little confused about what you should do with the absolute value once you take the derivative of arccsc on #28 for the book work on the turn in
ReplyDeleteThanks!
Laura Goo
Well you know that the square root of x is plus or minus x^1/2. Since this is between absolute value signs, only the positive answer is used. So basically drop the absolute value symbols and leave it a positive x^1/2. It will multiply later with another x^1/2 to just give you x.
Delete-Jenna Weed
Is it acceptable to leave a final answer as (e/5) or should we always estimate to 0.544? In other words, since the AP accepts both do you have a preference?
ReplyDeleteThanks,
Rachel Hersch
Exact is always best. Is it a calculator open problem?
DeleteHow should we explain why number 50b for the book work on the turn in doesn't contradict L'Hopitals Rule?
ReplyDeleteThanks,
Allison Honet
Can an endpoint on a closed interval be a local min/max as in number 11 of the book work on the turn-in?
ReplyDeleteThanks,
Rachel Hersch
Nope, because there are no points on one side of it, so it can't be greater/lesser than those nonexistent points.
Delete-Kai Selwa
I believe the answers at the end of our text say yes, an endpoint can be a local extrema. This is false, and other texts will show that. The AP follows what I taught, which is what Kai explained.
DeleteFor 1c on the turn in, can you assume that the dy/dt is the same as it was in 1b?
ReplyDelete-Julia Dickerson
I do not have my folder in front of me, so I cannot say yes or no outright. I advise you to ensure that both parts refer to the same curve at the same x and t values. If so, then yes, use the value from part b. Most parts of free response questions will rely upon values found in prior steps.
DeleteWhere can we find the answers to the Concavity worksheet?
DeleteThanks,
Katie Weitzel
Apparently they did not upload correctly to the website. I will have them available tomorrow in class.
DeleteThis week's board is now closed. No further comments will gain credit. Please use the week 7-8 discussion board now.
ReplyDelete