How to find umin(d,r) if xtanθ - (gx^2)/(2u2cos2θ) > r + √(r2-(x-d)2) for d-r < x < d+r ? And 0 < θ < π/2 , d and r can be any positive real number which d &g...

X goes from 0 to 2 Y goes from 0 to sqrt(4-x^2) Z goes from 0 to sqrt(4-x^2-y^2).   The function is zsqrt(4-x^2-y^2)dzdydx.   I know the conversion from rectangular...

The two surfaces defined by: xyz=a and (y/x)=b intersect in a space curve. Given a > 0 and b >0, find a general expression for the coordinates of the point on this curve that is closest to the...

How do I take partial derivative of something like this:   $$\sum_{i=1}^n\sum_{j=1}^nb_i(b_ja_{ij})$$   Both $b_i$ and $b_j$ is part of the same variable $b$, so...

I don't know what values to set for C in order to calculate for the y=??? function of the level curve

Describe the region bounded by the planes: x = 0, y=0, z=0, x+y=4, and x=z-y-1.   Describe as a region (in any order you can) the region inside the ball x^2+y^2+z^2=4 and...

Lagrange multipliers work great for finding the minimum value of y-ax, restricted to the curve y^2-x^2=1 for any a with 0<=a<1 (what is it?) but fails quite miserably if a >=1. Use the geometry...