Suppose R1,R2 are real numbers satisfying 0 < R1 < R2. A function is deﬁned in terms of polar coordinates by f(r,θ) =√(R1 + R2)r−r2 −R1R2.   (a) Show that the domain of...

a consumer buys 2 goods, the amounts of which are x and y. The marginal utility of consuming good x is Ux, while that of consuming good y is Uy. The 2 marginal utility functions are given by:    ...

a. Find the coordinates of the center of mass (centroid) of the portion of the cardioid r=1+cosθ above the x-axis; that is, the region described by R= {(r,θ) : 0 ≤ θ ≤ π, 0 ≤ r ≤ 1+cosθ}.    b...

The base of a solid in the region bounded by the parabola x2 + y = 4 and the line x + y = 2. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in...

Use your calculator to find the approximate volume in cubic units of the solid created when the region under the curve y = cos(x) on the interval [0,pi divided by 2] is rotated around the x-axis. 1 0...

Find the volume of the solid formed by revolving the region bounded by the graphs of y = x3, x = 2, and y = 1 about the y-axis.   93 times pi divided by 5 120 times pi divided by...

Suppose that, during the first year after its hatching, the weight of a duck increases at a rate proportional to its weight. The duckling weighed 2 pounds when it was hatched and 3.5 pounds at age...

The volume of a sphere is of radius r is v=4/3πr^2

A study of demand for air travel in Australia found that the demand (q) for discount air travel from Sydney to Melbourne depends on the airfare according to the equation q=55.2-.022p, where p is price...

a developer is running a freshwater pipeline from a water tower on the edge of a lake to a small resort community on an island 5 miles offshore it cost the developer 1.7 times as much to lay the pipe...

Peter can't remember the formula for the area of a circle. He decides to approximate the area of a circle by circumscribing a regular  18 -gon around the circle. If his approximation of the area...

I have to show that $f(x)={\frac{x}{|x|(1+x^2)}}$ is not differentiable at 0. I get to the point where $\lim_{h \to 0} \frac{1}{\left|h\right|\left(h^2+1\right)}$ and i check from both sides...

Part 1 - The type of bread chosen for this special calculus toast isn't the square sandwich shape, but the kind that is curved across the top. Imagine that the toast is composed of the curved part...