Calculus Answers

Find the center of the mass of the four particles having the masses of 2, 3, 3 and 4 kg and located at the points (-1, -2), (1, 3), (0, 5), and (2, 1), respectively.

derivative y = arctan⁴(3x⁵)

a. Find the volume V(S) of the solid S by revolving the region R bounded by x 2 + y − 4 = 0 and x − y + 2 = 0 about y = 0. (6 pts.) b. Set-up the integral that represents V(S) when the region R in (a.) is revolved about x = −2. (4 pts.)

1. Find the dimension of a rectangle with perimeter 200 m and whose area is as large as possible

2. The sum of two positive numbers is 10. Find the numbers if the sum of their squares is a minimum

find the surface area of the object obtained by rotating y=4+3x^2, 1<=x<=2 about the y axis

Let f(x)= x^2/x^2-9

(a) Find the intervals where f is increasing and decreasing. Identify the relative

extrema.

(b) Find the intervals where f is concave up and down and identify any inflection points.

(c) Sketch a graph of f using the information from this problem

Decompose

(i)

(x^2+X+1)/(X+3)(x^2-x+1)

into partial fractions (show all the steps).