Calculus Answers

Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is described by the formula below.
C(x) = 2500 + 4x + 0.02x2 + 0.0002x3

.

(b) Find C'(140).

Water is leaking out of an inverted conical tank at a rate of 10000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.

___________ cm3/min

A plane flying horizontally at an altitude of 7 mi and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 8 mi away from the station.

a. 219 mi/h
b.224 mi/h
c. 203 mi/h
d.223 mi/h
e. 208 mi/h

Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm2?

____________ cm2/s

A water trough is 5 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 100 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.1 m3/min how fast is the water level rising when the water is 20 cm deep?

_____________ m/min

Find the maximum and minimum values of the function f (x)= sin x + cos 2x in [0, 2pi] .

Find the area of the region enclosed by the curves x^2 = y and y = 1/2(x^^4 +x).

Estimate the are length of r(t) = (cos^2 t, sin 3t), t element of [0, pi] using trapezoidal rule with n = 6.

The lemniscates r^2 = a^2 cos 2 theta, revolves about a tangent at the pole. Show that the volume
generated is pi^2 a^3/4.

Find the length of the curve y = ln sec x between the points x = 0 and x = pi/ 3.