11.5#4

I am struggling with the problem question 4 in 11.5. 

The question regards the partial of w with a point.

So far I have input the variables for x,y,z 

Then I found the partial with respect to s then input the values given in the point. 

The value I calculated was 25.0855369231877 

Please help me out

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Ok, it looks like you did problem 3 correctly, and there were these nice chain rule formula on the bottom of that problem:

∂z/∂s = ∂z/∂x ∂x/∂s + ∂z/∂y ∂y/∂s  and  ∂z/∂t = ∂z/∂x ∂x/∂t + ∂z/∂y ∂y/∂t

You have to do exactly what you did there using those formulas, except now you have three variables so you'd so you'd need to go just a little bit further:

∂w/∂s = ∂w/∂x ∂x/∂s + ∂w/∂y ∂y/∂s + ∂w/∂z ∂z/∂s  

and 

∂w/∂t = ∂w/∂x ∂x/∂t + ∂w/∂y ∂y/∂t + ∂w/∂z ∂z/∂t

I can't tell exactly where you went wrong because YOU DIDN'T SHOW ME YOUR CALCULATIONS, but it *looks* like you actually tried to do that, and only tangled up in the algebra--on that score you would benefit from keeping the calculation of the separate terms in those sums separated and then only combine them once you've got them all done.

11.6#12

Hello Professor,

How do you go about finding the appropriate partial derivatives to define a tangent plane given a function that is not explicitly defined as f(x,y,z)= like in this case?

I already tried defining the equation as f(y,z)=x=(z+17)/e^ycosz and finding the partial derivatives of f with respect to y and z and obtained x=17+z. I also tried defining the equation as f(x,z)=y=ln(z+17)-ln(xcosz) and obtained y=-1/17x+1/17z. What am I missing here?

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Well, as we mentioned in class today, the gradient of a two variable function is perpendicular to the tangent line of a level curve.  Similarly, the gradient of a three variable function <∂f/∂x, ∂f/∂y, ∂f/∂z> is perpendicular to the tangent plane of the level surface. specifically the level surface L_17(f) for the function xe^y cos(z) -z .  This gives you a normal vector and the problem gives you a point in the surface, which is all you need for the equation of the tangent plane. I think this is covered on page 654 of the textbook FYI, unless this version of the text has moved it around.

11.3#10

Hello professor,
I’m working on 11.3 #10 and I’m not sure as to why I’m getting the partial derivative with respect to y wrong?

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well, because when you take the derivative with respect to a variable in a limit of integration, *that* variable gets substituted into the integrand.

11.3#11

I am very certain that the answer to this problem is 1, but this is not correct. Any advice?
Problem 11 11.3

*******************************Looks like you figured it out.  Just a small request though. When you ask me a question could you please tell me *what* you did instead of just the wrong answer that you got?

11.4#1

Hello Thomas,
I'm having difficulties in figuring out what I'm doing wrong in this problem. I followed the equation that is given in the book for finding the equation of a tangent plane to a surface and it keeps telling me it's wrong. I've tried a few different responses but they don't either.
Thanks

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Well, that because you haven't quite followed the equation as in the book.  For another approach, another way of writing the equation of the tangent plane is z=L(x,y), where L(x,y) is the linear approximation of f at the point (a,b)  given by that nice formula in the lecture notes for last Monday (the 18th):  z=L(x,y) = f(a,b) + (∂f/∂x)(a,b)(x-a) + (∂f/∂y)(a,b)(y-b).  If you had given me your calculation I could have told you more, but in your calculation you've dropped some minus signs on (∂f/∂x) and/or (∂f/∂y) and, I'm not sure how, miscalculated the right side of the equation.  

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Lecture Notes 2/18/19 through 2/22/19

Lecture Notes 2/18/19

Lecture Notes 2/20/19

Lecture Notes 2/22/19

Lecture Notes 1/30/19 through 2/15/19

Lecture Notes 1/30/19

Lecture Notes 2/1/19

Lecture Notes 2/4/19

Lecture Notes 2/8/19

Lecture Notes 2/11/19

Lecture Notes 2/13/19

Lecture Notes 2/15/19

Scores as of 2/13/19

Please note that 1) the grader has dropped the laptop that had your quiz 1 scores on it and is not sure if those scores can be recovered, and 2) that most people got a very good score on that quiz. Please tell me 

For discussion later (Tempe Butte)

10.7#16

Hi Professor,
I'm not really sure how to go about beginning this problem. I was hoping for some direction on where to start and how to execute problems like these.
Thank you

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It's easier than you're making it.  So you did part a) correctly. Here's your hint: if you replaced the 't' in part a) by some other linear function a*t + b to get r(a*t + b), for which t would r(a*t + b)=P and for which r(a*t + b) = Q?  Now in case (b) choose a,b to make the first time be 7 and the second time be 10.  Similarly 0, -4 for part c).

Practice exam complaint

Good afternoon Professor,

You said 10.9 would not be on the exam, but #3 asks about the velocity vector in part a as well asking for the acceleration vector which are both in 10.9. I remember in class you said #7 wouldn’t be on the exam, should we still be able to complete #3?
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Well, ok, you're right about that. It's kind of awkward, and the reason I didn't notice is, because that's the kind of problem I always put it because it's dead easy, but I'll have to replace it with something else.

hyperboloid of two sheets

x^2 + y^2 - z^2 = -1  OR  -x^2 - y^2 + z^2  = 1

hyperboloid of one sheet

x^2+y^2-z^2 = 1

hyperbolic paraboloid

z = x^2 - 2y^2

Elliptic Paraboloid

z=x^2 + 2y^2

Generic ellipsoid

4x^2 + y^2 + (1/4)z^2 = 1

Football (subtype of ellipsoid)

x^2+y^2+(1/2)z^2 = 1

Pillow (subtype of ellipsoid)

x^2+y^2 + 2z^2 = 1

Sphere

x^2+y^2+z^2 = R^2 (a subtype of ellipsoid)

10.5#10

Hi Professor,

Number 10 on 10.5 asks 

Determine whether the lines

L1:x=24+7t,y=21+6t,z=22+7t and L2:x=−13+8ty=−13+8tz=−19+10t

intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty.

I attached my work so you can see what I did so far. I came to the conclusion that those lines are skew and fail to see how they intersect even though ww says they do. 

Thank you for your help,

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It was just a simple arithmetic error. In fact going through your calculation it fooled me too at first.