Many and more students who study any branch in mathematics face a lot of troubles. And calculus is one of these problems. Trying hard to learn all the formulas the students finish up with a huge number of calculus questions that cause many problems in the studying process. We have worked out our service system so that you could get the calculus answers any time you need them with a minimum waste of time. If you have nobody to help you with the calculus problems – we are at your disposal!

Calculus

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

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

Calculus

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.

Calculus

Using the first principle, find the derivative of the function f (x) = 1 . (Show all workings and √x+1

state clearly, any theorem used)

state clearly, any theorem used)

Calculus

Find the Fourier series for the function

f(x) = (x-x)^2,-L < x < L

f(x) = (x-x)^2,-L < x < L

Calculus

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

Required:

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?

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

Required:

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)

Calculus

The demand function for a firm’s product is

q=150,000-75p

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?

q=150,000-75p

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?

Calculus

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.

Calculus

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.

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.

Calculus

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.