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


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?


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.

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

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.


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,


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.


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) = 〈2y3 − 6xz, 6xy2 − 4y, 4 − 3x2〉.

(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.


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