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Calculus

(x^3+y^3)=(3xy^2)dy/dx

Calculus

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 − x^{2}/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?

Calculus

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 − X^{2} / 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?

Calculus

Arcs of quarter circles are drawn inside the square. The center of each circle is at the corner of the square. If the radius of each arc is equal to 20 cm and the sides of the square are also 20cm. Find the area, in square cms, common to the four circular quadrants.

Calculus

Find the derivative for each function.

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

2.) y=7/9

Calculus

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

Calculus

Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by y=2x^2 and y=x^3 about the x-axis.

Calculus

Find the flux of ->F (x, y, z) =〈4x, 3z + x^2, (y^2)/2> across the positively oriented surface S given by ->R(u, v) = 〈2u, 4v, −u^2〉, 1 ≤ u^2 + v^2 ≤ 4,

Calculus

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.

Calculus

Find the work done in moving a particle along a curve from point A(1, 0, −1) to B(2, 2, −3) via the conservative force field ~F (x, y, z) = 〈2y^{3} − 6xz, 6xy^{2} − 4y, 4 − 3x^{2}〉.

(a) using the Fundamental Theorem for Line Integrals;

(b) by explicitly evaluating a line integral along the curve consisting of the line segment from A to P (1, 2, −1) followed by the line segment from P to B.