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Multiple choice: Find the volume of the solid that results when the region enclosed by the graphs of y=x^2 and y=2x is rotated about the x-axis

A:4/15 B:1/6 C:2pi/3 D:64pi/15

Three people live on the unit sphere and are going to walk from North 

Pole (0,0,1) to the South Pole (0,0,−1). The first person walks along the 

arc of a great circle that lies in on the coordinate planes. The second 

person walks along an arc of a great circle that does not lie in one of the 

coordinate planes, and the third walks along a curve that spirals once 

around the sphere. Find the parametric equations that describe possible 

paths for each person.  


Using the first principle, find the derivative of the function f (x) = 1 . (Show all workings and √x+1
state clearly, any theorem used)
Find the Fourier series for the function
f(x) = (x-x)^2,-L < x < L
A company estimates that the demand for its product fluctuates with the price it charges. The demand function is given as:
q = 100,000 - 200p

Where .q. equals the number of units demanded and .p. equals the price in rupees. The total cost of producing q units of the product is estimated by the function:

C = 150,000 + 100q + 0.003q2

a.Determine how many units of q should be produced in order to maximize annual profit?
b.What price should be charged?
c.What is the annual profit expected to equal?
determine the mass of the lamina corresponding to the first quadrant portion of the circle x^2+y^2 =25 where the density at thr point of (x,y) is f(x,y)=k*sqrt(x^2+y^2)
The demand function for a firm’s product is
Where q equals the numbers of units demanded and p equals the price in dollars.
Determine the price which should be charged to maximize total revenue.
What is maximum value for total revenue
How many units are expected to be demanded?
A closed cylindrical tin is of height h cm and radius r cm, its total surface area is A cm2 and its volume is r cm3. Find an expression for A in terms of r . Taking , find an expression of v in terms of r , hence determine the value of r which make v maximum.
A window consists of a rectangular piece of clear glass with a semicircular piece of
colored glass on top; the colored glass transmits only 1/2 as much light per unit area as the the clear
glass. If the distance from top to bottom (across both the rectangle and the semicircle) is 2 meters and
the window may be no more than 1.5 meters wide, find the dimensions of the rectangular portion of the
window that lets through the most light.
The temperature of an object is given by T ( t ) = 280 + 1.5 t 2 e − 0.12 t where t is measured in minutes and T is measured in Kelvins (abbreviated K). (a) Find the rate of change of the rate of change of temperature at the instant t = 20 minutes.
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