## Calculus Resources

Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. \$ 625p^2 - x^2...

The demand function for a certain make of ink-jet cartridge is the following where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. p =...

The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 3 in. long and increasing at the rate of 0.4 in./sec. How...

A 15-ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding down the wall at the instant of time when the bottom of the ladder is 9 ft from the wall and sliding...

Water flows from a tank of constant cross-sectional area 60 ft2 through an orifice of constant cross-sectional area 1/4 ft2 located at the bottom of the tank. Initially, the height...

The supply equation for a certain brand of radio is given as follows where x is the quantity supplied and p is the unit price in dollars. p = s(x) = 0.3√x + 15 Use differentials to approximate...

a. Find the volume of the solid region.   The solid above the parabolic region R={(x,y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1-x2} and between the planes z = 1 and z = 2-y   b...

Evaluate the following integrals:   a. ∫∫R (x+y) dA; R is the region in the first quadrant bounded by x=0, y=x2 , and y=8-x2   b. The solid in the first octant...

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...

1. Sketch each region and used double integral to find its area:   The region inside both the cardioid r=1-cosθ and the circle r=1   2.  Find the following average values   The...

The cost of manufacturing stuffed yellow cats is C(x)= 1/3x2 + 4x + 53 where x is the number of cats produced in thousands. The production level for the number of stuffed cats produced after...

The surface area of a sphere is decreasing at the constant rate of 5π cm2/s. At what rate is the volume of the sphere decreasing at the instant its radius is 4 cm?