12,3#10

I've tried almost two times to figure out what exactly this problem is
asking for in the incorrect box. I've tried a ton of different expressions,
and the generic f(r,theta), f(r,t), etc. I am just very confused as to what
exactly it wants as an answer.

I can handle picky problems, but this is
one silly demand here.

Any idea what is wrong with it?


Thanks!

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Sometimes webwork does picky, silly things, but this isn't one of those times. You  are given a function of x&y, f(x,y) You just decide to replace x by r and y by t, but that's not the way it works. Remember : x=r cos(t) and y = r sin(t), and you need to substitue these in for x&y.

Some things not to do (updated 10/27/16)

OK. I'm grading the exam and not pulling my hair out, but only because I don't have enough hair to do that. So, purely for your edification, I thought I would make a rogue's gallery of things not to do.

1) DO NOT REVERSE THE ORDER OF AN ITERATED INTEGRAL BY SIMPLY REWRITING THE INTEGRALS IN THE REVERSE ORDER.  (Limits of integration that are functions can never, ever,wind up in the outside integral.  

2) Do not simply change replace the variables in the limits of integration for the inside integral without changing the functional form.  This will never work either.

3) The antiderivative of a function is NOT the same as the derivative.  For instance 

∫ 1/(1+x^5)dx≠5x^4(1+x^5)^-2

4) 1/(a+b)≠1/a + 1/b.  NEVER, EVER.

5) Do not write a negative answer for an integral when the integrand is strictly non-negative on the domain of integration. <---NOTE: THIS IS A CHEAP WAY TO DETECT IF YOU DID YOUR CALCULATION CORRECTLY

6) When you are computing the value of an iterated integral, be sure you compute the antiderivative of the inside integral with respect to the inside variable,  for instance
∫_a^b∫_f1(x)^f2(x) x dy dx = ∫_a^b x y |_y=f1(x)^y=f2(x) dx = ∫_a^b x f2(x)-x f1(x) dx

but
∫_a^b∫_f1(x)^f2(x) x dy dx ≠ ∫_a^b 1/2 x^2 |_y=f1(x)^y=f2(x) dx = ∫_a^b 1/2(f2(x)^2-f1(x)^2) dx

Section 12.3 HW not due until next friday

Currently the homework 12.3 is due this Saturday and I was wondering if that was a mistake or not considering we have not gone over it yet and it's not on the test? Thank you for the clarification.

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Thanks for bringing this to my attention. I've moved the due date for section 12.3 back to Friday the 28th.

MAT Test 2 review materials

Excuse me Professor Taylor, but do you have any practice materials up for the second midterm?

Thanks!

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Same place (as noted on the syllabus): <https://math.asu.edu/resources/math-courses/mat267>

Estimated Grades as of 10/17/16

If I had to give you a grade today, these are the grades I would give you.  Here's how I figured it:  Since your final grade depends 50% on your three midterms, 25% on the final exam, 15% on the homework and 10% on quizzes and other activities, I gave a 75% weight to the one midterm you've taken 15% weight to your homework percentage and 10% to your quiz percentage.  Then I assigned grades on the principle <90%=A, <80%=B, <70%=C, <60%=D.  I did not bother to put +/- grades at this time.

11.6 #12

Hi Dr. Taylor!

I am not sure on how to take the partial derivative of
this function with x, y, and z variables.

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This question is designed to fool you.   :-)

Yes! If you try to treat this equation as the graph of a function of two variables, you'll wind up with a z on both sides of the equation, which will make you crazy.  Instead, just treat the surface as the 2-level surface {(x,y,z): f(x,y,z)=2} where f(x,y,z)=z(1-xe^y cos(z)).  Then you take partials with respect to z the same way you take any partial derivative. The equations for the tangent plane of a level surface of a function of three variables is covered n the textbook (remember that?) and in the lecture notes for 10/3/16.

11.6 #14

I have a question about the first part of this problem.

I have tried getting the gradient vector, composed of the partial derivative of Z with respect to x and Z with respect to y. I then made it a unit vector by dividing the vector evaluated at (1,1) by the magnitude. I then got this answer, which is incorrect.

Could I know what I am doing wrong?
Thank
you very much!

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The only thing you've done wrong is that you're giving the vector going up the mountain, while you need to go down.