Calculus Answers

Find the mass of the lamina in the shape of the portion of the plane with equation 4x + 8y + z = 8 in the first octant if the area density at any point (x, y, z) on the plane is δ(x, y, z) = 6x + 12y + z g/cm^2

use the method of cylinders to determine the volume of the solid by rotating the region bounded by y=-x^2-10x+6 and y=2x+26 about the

a. line x=2 b. line x=-1 c. line x=-14

use the method of disks to determine the volume of the solid by rotating the region bounded by y=10-2x,y=x+1 and y=7 about the

a. line x=8 b. line x=1 c. line x=-4

A poster is to have an area of 630 cm2 with 2.5 cm margins at the bottom and sides and a 5 cm margin at the top. Find the exact dimensions (in cm) that will give the largest printed area.

width : cm

height: cm

A ship is 20km west of another ship B. If a sails at 10km/hr. and at the same time B sails north 30km/hr. Find the rate of change of distance between them at the end of half hour.

Find the domain and range of the function (x,x/|x|).

A company manufactures and sells x televisions per month. If the cost and the

revenue functions (in dollars) are

C(x) = 72, 000 + 60x and R(x) = 200x − x²/30^,

respectively, with 0 ≤ x ≤ 6, 000, what will the approximate changes in revenue and

profit be if the production is increased from 1, 500 to 1, 505? from 4, 500 to 4, 505?

A company manufactures and sells x televisions per month. If the cost and the

revenue functions (in dollars) are

C(x) = 72, 000 + 60x and R(x) = 200x − X² / 30

respectively, with 0 ≤ x ≤ 6, 000, what will the approximate changes in revenue and

profit be if the production is increased from 1, 500 to 1, 505? from 4, 500 to 4, 505?

Find the derivative for each function.

1.) y=x^4-3x^3+5x^2-2x+1

2.) y=7/9

Problem 1: Use the tabular method to determine if the limits of the following functions exist:

a) lim𝑥→3 2/(𝑥−3)^2

b) lim𝑥→3 2/(𝑥−3)^3