Recent content by Cloudless

I used to be in the same situation. I hated small talk; everything I said seemed force and superficial, and my mouth hurt from fake smiling. Sometimes I meet someone I can easily carry a conversation with, and that's great. Not everyone connects easily. I used to worry about that but now...

I redid it in spherical coordinates. Much easier, but still missing a pi/2. I think the conclusion is the answer key was wrong. The question was ambiguous in its bounded area. I thought it was from negative pi/2 to pi/4.

1. Evaluate the integral ∫VxdV inside domain V, where V is bounded by the planes x=0, y=x, z=0, and the surface x2+y2+z2=1 Answer given: 1/8 - √2/16 (which is NOT what I got.. ) 2. The attempt at a solution Ok, it's a triple integral, I know this. ∫dx runs from 0 to 1 ∫dy...

Yeah, my mother gets really bad night terrors. :/ One time she woke the whole house saying there was someone standing outside the window. There were times where I'd be in bed, and my heart would be racing fast and inside I'm telling myself "wake up, there's something there", but my eyes would...

1. ∫∫∫E6xy dV, where E lies under the plane z = 1 + x + y Apparently according to a classmate, the limits are: -1≤x≤0, -1-x≤y≤0, and 0≤z≤ 1+x+y I know how to get z. But I am confused for y and x. To solve the limits of y, you would plug in 0 for z, getting y = -1 - x. But why is the...

That's exactly what the problem said. It wasn't a textbook question but created by the professor. I assume he meant direction in which the temperature decreases the fastest. By steps he meant the shortest distance a person would travel in the direction where the temperature decreases from 80...

If given only: f(5,2) = 80 fx(5,2) = 8 fy(5,2) = -6 Suppose 80 is measured in degrees Fahrenheit. Find the direction where the temperature would get cooler. I just did 8a - 6b = 0 (since using the dot product, <8,-6> * <a,b> = 0. Then I solved for a, b, and this was the vector equation. Then...

Ah ok. The notes never fully explained it so I was doing it by instinct mostly. xD Thanks

Homework Statement The given curve is r(t) = <t2, 2t, -3> Write an equation for the length of the curve from <0,0,-3> to <1, 2, -3> 2. The attempt at a solution I take the derivative of r(t) for r'(t), then plug it into the length formula. L = ∫ of √( (2t)2 + 22 ) For...

Wow, this is brilliant @_@ Thank you You would need a calculator for this method though, right? Inverse sin of (-1 to 1) = xy.

I come across questions where I have to match the equation with its contour map and graph. Examples: z = sin(xy) z = sin(x-y) Right now I'm using Wolfram Alpha for all of these, but supposing these appear on an exam... how do I graph it by hand? :confused: For example, for z =...

Say for the recursive formula 2, 5, 9, 19 , 37...Instead of writing it as an = an-1 + * 2 an-2 can you write it as: an = 2an + (-1)nJust double checking. I encountered this earlier helping someone and I haven't done recursive formulas in a while..

So if the second question was instead the same as the first ( For which x is the approximation sin(x) = x - (x^3)/6 correct within 1/100? ), I should be able to find an answer identical to the first answer? Steps: Same procedure for the 2nd example above. Instead, |R3(x)| ≤ 1/100, so...

So we had two examples in class, but I don't understand why they're different. And the professor is away today, which means I won't see him until the entire weekend has passed (a nightmare for students like me who obsess over a problem). 1. For which x is the approximation sin(x) ≈ x - (x^3)/6...

I would say the diameter would be the displacement in this case.