Tomorrow's Test! (a request)

Hello Dr. Taylor,

I had a question about tomorrows test. I was wondering if I could bring some blank graph paper in, to use as scratch paper. It will help me draw pictures to scale (for when switching limits of integration), and sometimes I like to write out the solution as it helps me figure out step by step what I need to do to solve the problem. Do you think this is a possibility? I will be okay with or without it. It just helps me draw my pictures which can be key to the answer. Let me know what you think. Thanks!

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I'd prefer to supply the scratch paper; the functions in the limits of integration will be very simple and any switching of limits of integration will depend on an understanding of these functions and their inverse functions and not on any precise rendering. 

Partial homework extension

I have extended the due date for section 12.5 to next Monday at midnight.

No cheat sheets allowed for the exam.

Would you be so kind as to let us have a HAND WRITTEN cheat sheet
with general formulas for ourselves? I think if you allowed us to have
example problems it would literally be cheating. But, perhaps if we could
have formulas like for linear approximation, and what information the
determinate tells us about our critical points. We could turn it in with
our tests so you know what was on there and that students don't share one
copy. I hope you take this into consideration as something allowed for this
test.

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Sorry, I asked the course coordinator and the rest of the instructors for this course, the consensus is that we cannot allow cheat sheets.

Lecture Notes 10/14/15 through 10/19/15

Lecture Notes 10/14/15

Lecture Notes 10/16/15

Lecture Notes 10/19/15

12.2 no 3

I'm having difficulty understanding how to solve this problem.  Where
should I start?

Well, the first step is to read section 12.2 in the textbook and the notes. The basic notion is that you are trying to write the double integral as an iterated integral.  For part (a), this means that you are integrating first with respect to y and then with respect to x, this means that you need to integrate from the horizontal line at the bottom of the triangle--which gives you the lower limit of integration of the inside integral, to the slanting line at the top of the triangle.  In order to do this, you *must* find the equation of the line relating from the graph of the line; this means that you write a linear equation. for y as a function of x. This function of x becomes your upper limit of integration.
For part (b) you must turn this around--the vertical line on the right gives you the lower limit of the inside integral, and the upper limit becomes the equation for x in terms of y that you get by solving the equation of the slanting line for x.

Section 12.1 no.1

Can you tell me what I'm doing wrong here?



















I  think so.  When dividing the square [0,2]x[0,2] into four equal squares you get squares [0,1]x[0,1], [0,1]x[1,2], [1,2]x[0,1], [1,2]x[1,2].  It looks like you misinterpreted the questions--for example in part (A) you have supplied the value of the integral

But you should instead give the value of the Riemann sum approximation for the integral 

with that partition of the square with values at the points (0,0),(1,0),(0,1),(1,1)

(25-0^2-0^2)ΔA_{11}+(25-1^2-0^2)ΔA_{21}+(25-0^2-1^2)ΔΑ_{12}+(25-1^2-1^2)ΔΑ_{22}

and since all of the ΔA's take the value 1, the correct answer for part (A) should be 

25+24+24+23=96

Review For Test 2!!!

The review for test 2 is in WEXLER 116 at 8:15pm on Oct 19th, 2015.