Calculus Answers

Question  9

If the production function is given by

Q = 300L − 4L,

where Q denotes output and L denotes the size of workforce, calculate the value of marginal product of  labour if L = 9.

a.        11

b.        46

c.        16

d.    146

8

The demand function of a firm is

Q = 90 − 1,5P,

where P and Q represent the price and quantity, respectively. At what price is revenue a maximum?

a.        15

b.        90

c.        30                                                             

d.        270

Find the centroid of the region bounded by the curves y= x³ and y=4x in the fourth quadrant. Sketch the bounded region.

find fx (x,y),fy(x,y),f,(1,3),and fy (-2,4) for the given function. If z=f(x,y)=3x3y2-x2y3+4x+9

Which functions are one-to-one on the domain (−∞,∞)

(−∞,∞)?

You may find it helpful to graph the functions and use the horizontal line test.

There may be more than one correct answer. Select all that apply.

• ψ(x)=sinx

• g(x)=x^3−5

• f(x)=x^2+1

• h(x)=x^5+x−2/x^4+1

• μ(x)=x^6+2x^2/x+1

• φ(x)=arctanx

1. The curve has an equation y = e^x. Compute the area bounded by the curve from x = 0 to x = 1.

2. The loop of the curve has an equation of y² = x(1 – x)². Find the area enclosed by the loop of the curve.

3. Given the area in the first quadrant bounded by y² = x, the line x = 4 and the x-axis. What is the volume generated when this area is revolved about the y-axis?

4. The region in the first quadrant which is bounded by the curve y² = 4x, and the lines x = 4 and y = 0, is revolved about the x-axis. Locate the centroid of the resulting solid of revolution.

5. The region in the first quadrant, which is bounded by the curve x² = 4y, the line x = 4, is revolved about the line x = 4. Locate the centroid of the resulting solid of revolution.

Find the surface area generated when the portion of the curve

y² = 12x from x = 0, x = 3 is rotated about the x-axis.

The parabolic reflector of an automobile headlight is 12 cm. in diameter and 4 cm. in depth. 

Find the surface area of the portion of the curve x² =4y from y =1 to y =2 when it is revolved about the y-axis.

Determine the tangent to the curve 3y² = x³ at (3,3) and calculate the area of the triangle bounded by the tangent line, the x-axis and the line x=3.