Calculus Answers

(1) If the total cost of a firm is c(x) = 1.5x^3 - 5x^2 + 20x + 5 . Find the marginal cost (in dollars) when 25 units are produced and sold. Where did you get the 3?

What use does Calculus have in the real world? Describe what part calculus plays in the real world with examples.

1.     The diameter of a right circular cylinder is equal to its altitude. Letting V and S be the respective volume and surface area of the cylinder and 2r the diameter, use differentials to estimate the maximum possible error, relative error, and percentage error in computing

(a)   the volume of this cylinder and

(b)  the surface area of the cylinder

when the measured diameter is 20 cm and the maximum possible error in the measurement is 0 1 cm.

Integrate (3-x^2)/(x^2+3)^2

The graph of the parametric equations is called a cycloid.

x=θ-sinθ and y=1-cosθ for 0≤θ≤2π

(a) find dy/dx

(b) find an equation of the tangent to the cycloid at the point where θ=π/3

(c) at what point is the tangent horizontal?

(d) graph the cycloid and the tangent lines in parts (b) and (c)

At a certain instant the dimensions of the rectangle are 8 and 12 feet, and they are increasing at the rates 3 and 2 feet per second, respectively. How fast is the area changing?

What is Integration? Discuss types of Integration with Example.