Calculus

Limits

100

Lim (x -> 0) F(x) F(x)=(Sin(x))/(x) No calculator. -_-

What is 1

200

Lim (x-> -4) F(x) F(x)=(x+3)^2012 No calculator. -_-

What is 1

300

Lim (x-> -1/2) F(x) F(x)=(3x^2)(2x-1) No calculator. -_-

What is -3/2

400

Lim (x-> infinity) F(x) F(x)=(1-cos(x))/x^2 No calculator. -_-

What is 0

500

Lim (x -> 0) F(x) F(x)=(((2+x)^3)+8)/(x) No calculator. -_-

What is 8

Derivatives

100

Find dy/dx of y=2x+1 No calculator. -_-

What is 2

200

Find dy/dx of y=(4x^-2)-8x+1 No calculator. -_-

What is (8x^-3)-8

300

Find an equation of the line normal to the tangent to the curve y=(x^3)-3x+1 at point (2,3). No calculator. -_-

What is y=(-1/9)x+(29/9)

400

Find dy/dx of F(x)=(sin(x)/1+cos(x))^2 No calculator. -_-

What is 2sin(x)/(1+cos(x))^2

500

Find dy/dx of f(x) = sin(pi(x^2) - x +1) No calculator. -_-

What is cos(πx² - x + 1) * (2πx - 1)

Volumes/Optimization

100

Area between the graphs of x=y^3 and x=y^2 Intersections at 0,0 and 1,1 No calculator. -_-

What is 1/12?

200

What is the smallest perimeter possible for a rectangle whose area is 16 in ^2 and what are its dimensions? No calculator -_-

What is Smallest perimeter-16 inches Dimensions-4x4 inches

300

An open top box is to be made by cutting congruent squares of side length x from the corners of a 20 by 25 inch sheet of tin and bending up the sides. How large should the squares be to make the box hold as much as possible? For extra 10 points-What would be the resulting volume of the box? Calculator allowed :)

What is x=3.68 inches extra 10 points-820.53 inches^3

400

Area between graphs y=2x^2 and y=(x^4)-2(x^2) Calculator allowed :)

What is 128/15

500

Find the area of the 'triangular' region in the first quadrant bounded on the left by the y-axis and on the right by the curves y=sin(x) and y=cos(x) Calculator Allowed :)

What is sqrt(2)-1 OR 0.414

Integrals

100

Integral of (x^3)+1 from -1 to 3 No calculator -_-

What is 24

200

Integral of (2-(1/x)) from 1/2 to 3 Calculator Allowed :)

What is 5-ln(6) OR 3.208

300

Integral of ((x^2)+(sqrt x)) from 0 to 1

What is 1

400

Integral of (2-(1/x)) from 1/2 to 3 Calculator Allowed :)

What is 5-ln(6) OR 3.208

500

dy/dx of the integral of ln(1+t^2) dt from 6 to X

What is -ln(1+x^2)

Related Rates

100

derivative of x^2+4x in respect to T

What is (2t)(dx/dt)+(4)(dx/dt)

200

The radius r and area A of a circle are related by the equation A=2(pi*r). white an equation that related dA/dt to dr/dt

What is dA/dt=2(pi*r)dr/dt

300

The radius R, height H, and volume V or a right circular cylinder are related by the equation V=pi*r^2*h Hoe id dV/dt related to dh/dt if R is constant.

What is dV/dt=pi*r^2^dh/dt

400

a police ruiser, approaching a right angled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight east. When the cruiser is 0.6 miles north of the intersection the car is 0.8 miles to the east. the police determine with radar that the distance between them and the car is increasing at 20 mph. if the cruiser is moving at 60 mph at the instant of measurement, what is the speed of the car?

What is 70 mph

500

A hot air balloon rising straight up from a level field is tracked by a range finder 500 feet from the lift off point. At the moment the range finders elevation angle is pi/4, the angle is increasing at the rate of 0.14 radians per minute. How fast is the balloon rising at that moment?

What is 140ft/min