Work, What is it good for?
The Integration Machine
The World Series
All You Can Eat
Buffet Style
Potpourri
100

Suppose a force of 10 N is required to stretch a spring 10 cm from its equilibrium position and hold it in that position. How much additional work is required to stretch the spring 25 cm if it has already been stretched 10 cm from its equilibrium position?

What is 2.625 J

100

Evaluate 

int x^2 cos(x^3 + e^2) dx

What is 

1/3 sin(x^3 + e^2) + C

100

Does

sum_(n=1)^oon^(-2/3)

 converge or diverge?


What is diverge?

100

Solve the initial value problem:

dy/dt = e^t/(2y)

, y(ln2) = 1

What is 

100

Find the area of the region bounded by the curves

y = x^2 - 2x

 and y = x + 4.

What is 125/6

200
A swimming pool has the shape of a box with a base that measures 25 m by 15 m and a depth of 2.5 m. How much work is required to pump the water out of the pool when it is full? The density of water is 1,000 kg/m^3.
What is 11,484,375 J
200

Evaluate 

int tan(x) sec^3(x) dx

What is 

1/3 sec^3(x) + C

200

Does

sum_(n=1)^oo 2^n/e^n

 converge or diverge?

What is converges by root test.

200
Find the centroid (center of mass) of the region bounded by the curves y = x and y = x^2.
What is (1/2, 2/5)
200

Find the volume obtained by rotating the region bounded by

y = x^3

 and

x = y^3

 about the x-axis.

What is 

(16pi)/35

300
A 30 m long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and that the chain has a density of 5 kg/m. How much work is required to wind the chain onto the cylinder if a 50 kg block is attached to the end of the chain?
What is 36750 J
300

Evaluate 

int x^3 ln(x) dx

What is 

1/4 x^4 ln(x) - 1/16 x^4 + C

300

Does

sum_(n=1)^oo 1/(sqrt(n)sqrt(n+1))

 converge or diverge?

What is diverges by the limit comparison test.

300

The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the Golden Gate Bridge in San Francisco is 1280 m long and 152 m high. The parabola

y=0.00037x^2

 give a good fit to the shape of the cables, where |x| <= 640, and x and y are measured in meters. Approximate the length of the cables that stretch between the tops of the two towers. Round to the nearest meter.

What is 1326 m

300

Find the volume of the solid obtained by rotating the region bounded by

y = x^2 + 4

 and

y = 12 - x^2

 about y = -1

What is 

384pi

400

Evaluate 

int x/(x^2 + 2x - 3) dx

What is 

3/4 ln(x + 3) + 1/4 ln(x - 1) + C

400

Does

sum_(n=1)^oo n^5 e^-n

 converge or diverge?

What is converges by the comparison test.

400

Find the area enclosed by one petal of the four-leaf rose 

r = 2cos(2theta)

What is 

pi/2

400

Find the interval of convergence of the series 

sum_(n=1)^oo (-1)^n x^n/(n + 4)

What is (-1,1]

500

Evaluate 

int_0^1sqrt(4 - x^2) dx

What is 

sqrt(3)/2 + pi/3

500

Does

sum_(n=1)^oo (-1)^n/(n^2 - 1)

 converge absolutely, converge conditionally, or diverge?

What is converges absolutely by the limit comparison test.

500

Find the equation of the line tangent to the curve given by the parametric equations x = tcos(t), y=tsin(t) at

t = pi

.

What is 

y = pi x + pi^2

500

Find the first 4 non-zero terms of the Taylor Series for f(x) = lnx centered at a = 1.

What is 

(x-1) - 1/2 (x-1)^2 + 1/3(x-1)^3 - 1/4 (x-1)^4 + ...

M
e
n
u