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Limits
Derivative
First Derivative Test
Related Rates
Challenge
100
What is the limit as x -> of 4/x
0
100
Find the derivative of x^3
3x^2
100
Find the derivative of x^2
2x
100
y = sqrt(x) find dy/dt when x = 4 Given dx/dt = 3
3/4
100
Name the famous mathematician who came up with this formula e^i*pi - 1 =0
Euler
200
What is the limit as x -> 0 of sin(x) / x
1
200
Find the derivative of f(x) = t^2 * sin(x)
t^2 * cos(x) + 2t*sin(x)
200
Find the interval on which the function is increasing. f(x) = x^2 - 8
(4, inf)
200
The radius of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area when r = 37 centimeters.
296 * pi cm^2 / min
200
Who created calculus?
Newton and Leibniz
300
Limit x -> inf of x^4 + 3x^3 - 4x^5 + 3x^4 / 5x ^3 + 3x^4 - 5x^5 + 2x^4
4/5
300
Write out the rule for the derivative of the following function f(g(h(x)))
f'(g(h(x))) * g'(h(x)) * h'(x)
300
On which intervals is the function increasing or decreasing? f(x) = 2x + 1/x
Increasing (-inf , -sqrt(2) / 2) and (sqrt(2) / 2 , inf) Decreasing (-sqrt(2)/2 , sqrt(2) / 2)
300
All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is 2 cm?
72 cm^3 / sec
300
What 4 things do we need to create a distance metric
d(x,y) = d(y,x) d(x,y ) > 0 d(x,y) = 0 then x =y d(x,y) + d(y,z) >= d(x,z)
400
Limit x -> 9- of 6/ 9-x
inf
400
Find the derivative of the function f(x) = sqrt(x) / (x^3 + 1)
1 - 5x^3 / (2sqrt(x)(x^3 + 1)^2
400
Identify all relative extrema of f(x) = x - 2sin(x)
Max at 5 * pi / 3 Min at Pi / 3
400
A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?
25/3 ft/sec
400
To which ancient civilization do we owe time being measured in a number system which is base 60?
The Babylonians
500
Limit h -> 0 of f(x+h) - f(x) / h
Tangent Line
500
Derivate of cot(x) * sec(x)
-cot(x) csc(x)
500
A fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water. At what rate is the angle theta between the line and the water changing when there is a total of 25 feet of line from the end of the rod to the water.
0.017 rad/sec
500
Name the Mathematician who developed Ring Theory then was shot the next day in a duel.
Évariste Galois