Derivatives
Trigonometry
Limits
Applications!
Integrals
100
What is a derivative?
The instantaneous rate of change of a function!
100
What is the value of sin(30°)?
0.5
100
the limit as 3x+2 approaches 2 is
8
100
Daniel is filling up a bucket with water at a rate of 3t liters per minute. In 5 minutes, how much water will there be in the bucket?
37.5 liters
100
Solve∫x2 dx
x3/3 +C
200
When using the difference quotient what variable gets cancelled out?
h
200
What is the coterminal angle made with -315° angle?
45°
200
Piecewise function has a jump discontinuity at x=3. Why limit does not exist?
left-hand limit and right-hand limit are different
200
A farmer has 1000m of fence for his pigs pens. What's the largest area of space he could have for his pigs?
62,500 m2
200
Solve ∫02 (x2+1) dx
14/3
300
What is the derivative of the function at f(0)? 
The derivative does not exist
300
Given csc(θ)= 2, sin(θ) =
0.5
300
if f(a) is defined and the limit as x approaches a exists, what is the limit?
f(a)
300
Given x3-6x2+9x what are the critical points?
1 & 3
300
Solve ∫31 1/x dx
ln(3)
400
Given ln(x) what is the derivative?
1/x
400
What function is this graph of?
y = cos(θ)
400
the limit as sin(x)/(x) approaches 0 is
1
400
A square is growing so that each side increases at a rate of 2 cm per second. When the side length is 5 cm, how fast is the area increasing?
20cm/s
400
What is the area between y=x2 and y= 4 from -2 to 2 ?
32/3
500
What is the derivative of ex
ex
500
Give all possible solutions to sinθ = 0.5
θ=pi/6±2kπ and θ=11pi/6±2kπ
Where k is an integer
500
How would squeeze theorem help us find the limit of x2cos(1/x) as x approaches 0?
will write explanation out, answer is 0
500
A box is being built with a square base and no top. If the volume is 100 m3 find the dimensions that minimize surface area.
sides = cubic root of 200, height = 100/(cubic root of 200)2
500
A particle moves at a velocity of v(t) = t2+1. Given this find the displacement from t= 0 to t = 3
12