Find any critical numbers of the function.
f(x)=x³-3x²
What is x=0, x=2?
100
When finding an indefinite integral, this needs to be added to the answer.
What is +C?
100
The limit of (sinx)/x as x approaches 0.
What is 1?
100
Find the area of the region bounded by the graphs of the equations.
y=5x²+2, x=0, x=2, y=0
What is 52/3?
100
Use the Second Fundamental Theorem of Calculus to find F'(x).
F(x)=⌠(t²-2t)dt Upper Bound: x Lower bound: -2
What is F'(x)=x²-2x?
200
Identify the open intervals on which the function is increasing or decreasing. y=x√(16-x²)
What is Increasing (1,∞) and Decreasing (-∞,1)?
200
Find the indefinite integral. ⌠(2x-3x²)dx
What is x²-x³+C?
200
The limit of (4+3/x) as x approaches ∞.
What is 4?
200
Use left endpoints and the given number of rectangles to find an approximation of the area of the region between the graph of the funtion and the x-axis over the given interval.
f(x)=cosx, [0,π/2], 4 rectangles
What is about 1.1835?
200
Find the value(s) of c guaranteed by the MVT for Integrals for the function over the given interval.
f(x)=√x, [4,9]
What is about 6.4178?
300
Determine the open intervals on which the graph is concave upward or concave downward. g(x)=(x²+4)/(4-x²)
What is Concave upward: (-2,2) and
Concave downward: (-∞, -2), (2,∞)?
300
Evaluate the definite integral.
⌠2sin(πx)dx Lower Bound: 0 Upper Bound: 1
*π is pi
What is about 1.273?
300
The limit of (5x²)/(x+3) as x approaches -∞.
What is -∞?
300
Find the area of the region.
f(x)=3+√(x), g(x)=½(x)+3
What is 4/3?
300
Find dy/dx by implicit differentiation.
tan(x+y)=x
What is -x²/(x²+1)?
400
Explain what the first and second derivatives can find.
What is Increasing/decreasing, extrema, concavity, and points of inflection?
400
Find the average value of the function over the given interval.
f(x)=x³ [0,1]
What is the average value= ¼?
400
The limit of sin2x/x as x approaches ∞.
What is 0?
400
Find the volume of the solid generated by revolving the regions bounded by the graphs of the equations about the x-axis.
y=√x, y=0, x=3
What is 9π/2?
400
Determine the open intervals on which the graph is concave upward or concave downward.
f(x)=-x³+6x²-9x-1
What is Concave upward: (-∞,2) and concave downward: (2,∞)?
500
Find the slope of the tangent line to the graph of the function at the given point. g(x)=x²-9, (2,-5)
What is m=4?
500
Find the indefinite integral.
⌠x²(x³-1)⁴dx
What is 1/15(x³-1)⁵+C?
500
Find the limit (if it exists). If it does not exist, explain why.
The limit of x/(√(x²-9)) as x approaches -3 from the left.
What is Limit does not exist, The function decreases without bound as x approaches -3 from the left?
500
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y=4.
y=3/(1+x), y=0, x=0, x=3