# *UNSORTED

- Applied Optimization Problems · Calculus
- Green's theorem example 1 (video) Khan Academy
- mathispower4u Calculus III
- mathispower4u Calculus III
- Volume and Average Height
- Stokes' theorem examples Math Insight

# Green theorem example rectangular pool

Note that as x. You then cut equal-size squares from each corner so you may fold the edges. Let V. Find the volume of the pool. The lifeguard swims with a speed v.

Video: Green theorem example rectangular pool Green's Theorem

Green's Theorem on a rectangle. Suppose rectangle D = [a, b]×[c, d].

### Applied Optimization Problems · Calculus

Example Let C be the triangle with vertices at (0,0), (1,1), and (0,1), with positive. Examples illustrating how to use Stokes' theorem. Stokes' theorem relates a surface integral of a the curl of the vector field to a line integral of the vector field.

ing examples would be soon incorporated. Vector forms of Green's Theorem. A swimming pool is circular with 40–ft diameter.

If the maximum value occurs at an interior point, then we have found the value x.

### Green's theorem example 1 (video) Khan Academy

Suppose a visitor swims at the rate of 2. Glossary optimization problems problems that are solved by finding the maximum or minimum value of a function. If the absolute maximum occurs at an interior point, then we have found an absolute maximum in the open interval. For example, in [link]we are interested in maximizing the area of a rectangular garden.

We can divide the rectangle into a grid, m subdivisions in one direction and n in. some two-dimensional version of the Fundamental Theorem of Calculus, but. Example Figure shows the function sin (xy)+6/5 on [ Ex A swimming pool is circular with a 40 meter diameter.

Example Find the maximum and minimum values of f(x)=x2 on the interval Theorem (Extreme value theorem) If f is continuous on a closed interval [a ,b]. since the perimeter is twice the length plus twice the width of the rectangle. Ex You are standing near the side of a large wading pool of uniform. More specifically, Green's theorem in the plane allows you to transform For example, the boundary curve of a square is piecewise smooth.

## mathispower4u Calculus III

It consists of four . of swimming in a big round pool in which the water is rotating as in a whirlpool .

Thinking of the loaf of bread, this corresponds to slicing the loaf in a direction perpendicular to the first. Step 2: The problem is to maximize R.

Step 1: Draw a rectangular box and introduce the variable x to represent the length of each side of the square base; let y represent the height of the box.

## Volume and Average Height

In this example there is no particular reason to favor one direction over the other; in some cases, one direction might be much easier than the other, so it's usually worth considering the two different possibilities. Suppose the dimensions of the cardboard in [link] are 20 in.

Therefore, we consider V. For every continuous nonlinear function, you can find the value x.

Maximizing Revenue. Let S denote the surface area of the open-top box.

Determine the maximum area if we want to make the same rectangular garden as in [link]but we have ft of fencing.

In the previous examples, we considered functions on closed, bounded domains. Determine the maximum area if we want to make the same rectangular garden as in [link]but we have