Turn in #13 is due Wednesday, Feb.3, 2015!
This is for discussing assignments from WEEK 7-8, including homework,
turn-in #13, in-class
work or lessons, or anything else related to the
class from these weeks. Please be sure to include your
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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!!!).
Hey,
ReplyDeleteWhen finding the volume of a shape revolved around a line, we're supposed to use the washer method, and if that doesn't work, then use the lateral surface area method( I can't recall the proper name, sorry), correct?
Rafey
Yes, if the washer method doesn't work becasue the outside and inside functions are the same, then you can use the shell method (the cylinders).
Delete- Daniel H.
Do we keep the function in terms of x if it is being revolved around the x-axis or the y-axis? Thank you!
ReplyDelete-Maggie Hammond
If you are finding the volume of a solid of revolution, your integral will be in terms of x when you're revolving the function around the x axis or a y=k horizontal line (k being a constant). If the function is revolved around the y axis or an x=k vertical line, the integral will be in terms of y.
DeleteHope that helped!
Anne Kozak
Anne is correct, as long as you are using washers. Think about the geometric shape you are using (washer vs shell) and think about the thickness of a single cross section, this will either be a dx or dy. this is what tells you what variable to integrate with respect to.
DeleteWould we need to be able to find the intercection points algebraically and solve for volume or will we always get a calculator for these problems
ReplyDeleteIf a problem requires an algebraic solution to finding the intersection of two curves, it is typically a straight forward quadratic or trigonometric equation. The AP isn't concerned with testing your ability to find points of intersection, rather that you know the points are necessary to properly set up the integral.
DeleteIs it possible to use cylindrical shells when you have two functions?
ReplyDeleteThanks,
Rachel Hersch
Yes. You may need to use separate integrals for each function, or use the difference between the functions as your height.
DeleteDo we need to find the equation of line l for problem 1 on the turn-in?
ReplyDeleteThanks,
Allison Honet
Yes, you will need it at some point.
DeleteFor problem 3 on the turn-in, is the parabola's vertex at (0,0) or is that just one of the points on the parabola?
ReplyDeleteThanks,
Katie Weitzel
it must be the vertex because the parabola is symmetrical to the y-axis
DeleteIs region S the area from line l to f(x), or does it get cut off at the x-axis?
ReplyDeleteS is the ENTIRE shaded region in quadrants I and IV.
DeleteHey Mr. Wilson, I wasn't sure how to find the length of a curve, is that something we should be able to find with the skills we have or is it something we are going to learn next week?
ReplyDeletethanks,
Will Schwartz
Curve length is in section 7.4. We are covering it Tuesday, but read below.
DeleteEnjoy your snow day on Monday. Please read Section7.4 on lengths of smooth curves, as well as this link: http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx.
ReplyDeleteTurn In #13 is still due Wednesday. We will also have a quiz on Volumes Wednesday.
As Intweeted last night, since we have a second day off the turn in and quiz will be pushed back to Thurs. please read 7.4 and the link above regarding arc length prior to Wednesday's class.
DeleteFor number 2c on the turn in where we have to find the length of the boundary of R, does it mean the whole three-sided boundary, or just the curve?
ReplyDeleteThanks,
Matthew MacMichael
It is all sides of the region, not just the side defined by the function.
DeleteHi folks,
ReplyDeletePayton is sick and requires a day home from preschool tomorrow. As such, I will have to remain home with her as well. Please refer to the examples in the text and the link above regarding arc length (I especially like the examples integrating with respect to y). It is fairly straight forward - in fact, we essentially proved where the formula comes from last week when we looked at surface area. The homework is: p.399 #11-21odd, 22, 24, 28, 30.
Turn in #13 is due Thursday.
We will have a quiz on volumes Thursday, as well.
I hope your daughter gets well soon, coach!
DeleteRafey
For number 1A on the turn in, is it appropriate to use the washers method? Is it possible to use cylinders?
ReplyDelete-Kelsey Nowak
Either method will work here.
DeleteWill we be allowed to use a calculator on the quiz Thursday?
ReplyDeleteThanks,
Laura Goo
No, it will be a non calculator quiz
DeleteWhen is it easier to use shells instead of washers? Should we always try to use washers to begin with?
ReplyDeleteThanks,
Lexi Kizy
M approach is to always try using washers. If I have a situation where the same curve forms the inner and outer radius, then I will go to cylindrical shells. Also, if washers are horizontal, requiring integration with respect to y, and the function isn't easily solved for x as a function of y, then I will use cylinders.
DeleteIs arc length on quiz??
ReplyDeleteThanks,
Eva A-L AND Julia Berthel
No, just volumes and surface areas.
DeleteDo the shell and washer methods usually show up on the calculator or non calculator sections of the AP test?
ReplyDelete-Amanda Bachand
Both.
DeleteWill we be given a visual of the graphs on the quiz tomorrow?
ReplyDeleteThanks,
Rachel Hersch
Yes.
DeleteFor 3b on the turnin when you are solving the integral, can you put b in for x if there is already a b in the equation that you are taking the anti derivative of?
ReplyDeleteThanks,
Emma Gijsbers
I would use a different variable for your upper limit of integration to avoid confusion.
DeleteFor non calculator problems, are we more likely to just have to set the equation up? Also, if the integral is in terms on x or y respectively, do we always have to write dx or du at the end of the integral?
ReplyDeleteThanks
Sarah Fried
Most of the time it is merely a set-up type problem, as the antiderivatives are not able to be done analytically. And yes, YOU MUST ALWAYS DENOTE THE VARIABLE OF INTEGRATION!
DeleteDx or dy ***
ReplyDelete