Turn in #10 is due Thursday, Jan. 26, 2017!
This is for discussing assignments from WEEKS 7-8, including homework,
turn-in #10, the MIDTERM EXAM, in-class
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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
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credit!!!)
As a reminder: Turn In #10 is due Thursday 1/26/17.
ReplyDeleteThe midterm exam will be formatted as follows:
Friday 1/27/17: Multiple Choice sections (calculator & non-calculator)
Monday 1/30/17: Take home Free Response sections due
Review materials are on the website (disregard the section describing the midterm format on the handout).
For bookwork problem 26, because the discontinuity occurs at zero, that's where I should set my limit in order to solve, correct?
ReplyDeleteDahvi Lupovitch
Yes, but make sure it is 0^+, because you have to include which side it is approaching 0 from.
DeleteAndrew Saad
For 1b, because it's asking with respect to y, will my interval be y values? So it would be from [0,2] or is it the same as 1a?
ReplyDeleteYeah, look at it from the y values, so from [0,2]. You can physically turn the paper and look at it from the y direction.
DeleteFor the Turn in problem 1C, in the "2y" they refer to as the height, is the y part just re-solving for both functions (f and g) in terms of y and then subtracting them?
ReplyDeleteBecause it's perpendicular to the y-axis it must be integrated in terms of y. So yes, resolve f and g for in terms of y and then you do height (2y) times the width (the equations subtracted *top - bottom*) times, which is area, times dy which turns it to volume. Make sure you switch your limits.
Deletefor 1b on the turn in, do we have to change the limits to integrate with respect to y?
ReplyDeleteYes, you do. As opposed to integrating from 0 to 6, now you have to integrate from 0 to 2.
DeleteDoes 3 need an actual explanation or is the work itself enough to prove the answer?
ReplyDeleteI assume you still need to explain in words.
DeleteAndrew Saad
There are no parts to problem three that require written explanation, but it never hurts to include one.
DeleteDoes the work for solving b need to be written out even though it should have the same answer as 1a?
ReplyDeleteYes, you need to show the anti-derivative with end values substituted in.
DeleteFor 1c and 1d can the dy be replaced with the heights or do you have to solve deferentially?
ReplyDeleteAndrew Saad
1c provides you with the height in terms of y, but the height is NOT dy. dy represents the 3rd dimension value (call it depth or "thickness" if you will). Also, the value in part c is not applicable to part d.
DeleteTurn In #10, problem 5c, you MAY use a calculator to evaluate this definite integral. Although, you SHOULD be able to do this by hand (expand the trinomial^2 and power reduce the sin^2 term).
ReplyDeleteFor number 26 in the bookwork, is there a special trick in order to find a converging value?
ReplyDeleteDon't have my book with me here...sorry.
DeleteFor 1c on the turn in, what do you have to do with the height of 2y?
ReplyDeleteYou need this for finding the area of a cross section.
DeleteOn turn in problem 5b do we need to find the places where y=-2 intersects the function (for the limits of the integral) or can we just use values a and b because I'm having trouble finding the actual values by hand.
ReplyDeleteYou may use arbitrary values as long as you define the,. Since part c is open for calculator use, you may use a calculator here as well to find the values if you wish.
Deleteif you rearrange the shape in 5 so it is just under the x axis will the volume solved for be the same as the original or would it come out different? I know the area would be the same but I'm not sure if it changes the heights of the squares and makes it a different volume.
ReplyDeletein other words, is there an easier way todo 5c then to multiply out the subtracted function squared and getting a really long mess of stuff?
DeleteSinusoids are symmetrical. Feel free to use this property whenever it seems useful.
DeleteThursday's class period is for review and exam preparation. You may also utilize some of it to complete the turn in. You must turn in your turn in by the end of class on THURSDAY.
ReplyDeleteThank you!!!!!
DeleteOn the turn in, question 5B, should we leave the limits of the integral in terms of A and B due to the problem being no calculator?
ReplyDeleteYeah, you would have to do that since the problem is no calculator.
DeleteYes, just leave it in terms of a and b
ReplyDeleteIn 2c, when you take ln(b/(sqr1+4b^2)), what happens? Will it simply converge or will the ln affect the final outcome?
ReplyDeleteYou can use L'Hopital's and get 1/b over 1/(math stuff) and that simplifies, which ultimately converges.
DeleteChance Stephenson
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ReplyDeleteHow should we justify our answer for #3 on the turn-in? Will explaining the process be enough to count for points?
ReplyDeleteFor #3, make sure you have sufficient and clear work shown, that leads logically to the answer. After you have the work, I'm guessing it wouldn't be a bad idea to give a written explanation as well, but I'm not positive.
DeleteI'm pretty sure if you just show the work that you used to get to your answer clearly that's enough of a justification.
DeleteFor 4a, what do we use for y?
ReplyDeleteChance Stephenson
Use the y-value given with the initial condition to plug in for the derivative
DeleteFor 4a, look at the given initial condition when x=0, which is also the same x value as the limit is approaching.
DeleteFor 5b on the turn in, how are you supposed to find only the area of R that is below the line y=-2? Can you subtract x^3-4x from -2?
ReplyDeleteYou can find the integral from where y=-2 intersects with the function and use those points to make a rectangle that you subtract from the whole integral. This gets rid of the R that is above the line.
DeleteFor 1c would we just plug 2y straight in for height rather than solving for some expression for height?
ReplyDeleteyes you don't have to square the original area, it provides 2y as the height so you multiply that by the area
DeleteYes just plug 2y in because you're findin the volume for values perpendicular to the y axis so you're using dy
ReplyDeleteCan anyone explain how one of the functions diverges but when it's combined with another function it converges?
ReplyDeleteThe two functions are diverging in opposite directions, but at the same rate, so when they're combined they cancel out and L'hopitals can be used to reach a converged output
DeleteWhen you are finding if a improper integral diverges or converges, how do you know if it's approaching 0 at a fast enough rate to converge instead of just diverge?
ReplyDeleteYou must take the limit of the anti derivative as the end point approaches the value causing the "improperness." If the limit exists as a finite value, the integral converges. If not, then it diverges.
DeleteClarification for the midterm... on question 1b, is it asking for the TOTAL gallons entering the tank (taking into account the amount leaving), or is it just asking for the amount entering (disregarding the amount leaving)?
ReplyDeleteOnly the amount entering, not considering amount leaving.
DeleteAlso for the midterm, on 3a, do we have to solve for k, the growth constant? Or can we keep it in the differential and then solve for it in 3b?
ReplyDeleteOnce found in part b, you should replace this value in part a.
DeleteFor 3c when solving for dy/dt and d2y,dt2, should we use the chart value of population in 1940, or the value that we calculated in part c as the approximation in 1940 (using the model from part b)?
ReplyDeleteThis comment has been removed by the author.
DeleteThe model's value. This is what you are determining the concavity of. The table value may not even lie on the model curve.
DeleteFor problem 1 on the midterm, is the whole sine function squared in f(t) [(sin(t/pi))^2], or is (t/pi) squared while sine isn't being raised to a power [(sin((t/pi)^2))^1]?
ReplyDeleteIt is the latter. You should be familiar with this notation.
DeleteFor the explanation in part 2d is drawing tangent lines enough proof along with an explanation?
ReplyDeleteYour explanation should be founded upon the calculus in the parts above.
DeleteLet me remind everyone that you may ask clarification of directions questions only for the midterm. Do not discuss specific details or "how to" here. Don't forget to adhere to and sign the honor pledge before turning in your take home.
ReplyDeleteFor 1a does the ^2 apply to the t/pi or the whole quantity of sin(t/pi)
ReplyDelete1b*
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