Limits
Anti-Derivatives
Properties, Rules, and Theorems
Area
Position, Velocity, Acceleration
100
Evaluate Lim 6x-3 as x -> 4
What is 21?
100
Integrate F'(x)=x^2
What is x^3/3+C?
100
Product Rule
What is f'(x)g(x)+f(x)g'(x)?
100
A=integral from a to b of (upper function) - (lower function) dx
What is the formula for finding area between two curves? ?
100
d(t)=2t^3 - 3t^2 -12t + 8 find displacement at t=0
What is 8?
200
Evaluate Lim sin(x)/x as x -> 0
What is 1?
200
Integrate F'(x)=3x^2+6x
What is x^3+3x^2+C?
200
Chain Rule
What is f(g(x))= f'(g(x))g'(x)?
200
Find the area bounded by the graphs of the following: f(x)=x^3 and g(x)=x
What is 1/2?
200
The velocity equation if height of S=160t-16t^2
What is v(t)=160-32t?
300
Evaluate Lim (abs(x-4))/(x-4) as x -> 4
What is no limit?
300
Integrate F'(x)=x^3-3x^2+7x+8
What is x^4/4-x^3+7x^2/2+8x+C?
300
L'Hospital's Rule
What is lim f(x)/g(x) = lim f'(x)/g'(x)?
300
Find the area bounded by the graphs of the following: f(x)=x^2 and g(x)=x^3
What is 1/12?
300
The acceleration of a particle whose position is x(t)=2t^3 -21t^2 +60t + 3
What is a(t)= 12t - 42?
400
Evaluate Lim (x^2-9)/(x+3) as x -> -3
What is -6?
400
Integrate F'(x)=x/(sqrt(1-x^2))
What is -sqrt(1-x^2)+C?
400
Mean Value Theorem
What is f'(c)=(f(b)-f(a))/(b-a)??
400
Find the area bounded by the graphs of the following: f(x)=x^4 and g(x)=x^5
What is 1/30?
400
x(t)=t^3 -9t^2 + 24t Find when particle changes direction.
What is t=2 and t=4?
500
Evaluate the Lim (3x^3+4x^2+7)/(5x^2+6x^3) as x -> infinity
What is 1/2?
500
Integrate x/(4+x^2)^.5
What is (4+x^2)^.5+C?
500
Trapezoidal Rule
What is Area≈1/2(y0+y1)Δx+1/2(y1+y2)Δx+1/​2(y​2+y3)Δx+…?
500
Find the area bounded by the graphs of the following: f(x)=5x^2 and g(x)=5x^3
What is 5/12?
500
The position of a particle whose acceleration is a(t)= 12t^2-42t-62
What is t^4-7t^3-31t^2?
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