Limits
Derivatives
Anti-Derivatives/Integrals
Theorems/Rules
Misc/History
100
What does it mean if the left limit and the right limit are different?
A limit does not exist
100
Name 4 derivative rules
Power Rule, Quotient Rule, Chain Rule, Product Rule.
100
What is the antiderivative of f(x)=cos(x)
f(x)=sin(x)
100
What is the intermediate value theorem
The intermediate value theorem states that there must be at least one value c within [a, b] such that f(c) = w
100
What two people helped create the study of calculus?
Issac Newton and Gottfried Leibniz
200
What type of discontinuity is a vertical asymptote
Infinite Discontinuity
200
Solve for the derivative
f(x)=(4x)^2
f'(x)=32x
200
What is the antiderivative of f(x)= sec^2(x)
f(x)=tan(x)
200
What are the three main theorems in Calculus?
The intermediate value theorem, extreme value theorem, and mean value theorem.
200
If a function is not continuous then it cannot be what.
Differentiable
300
Solve the limit
4x+3 as x approaches 3
15
300
Is a derivative the slope of the secant line or tangent line?
Tangent Line
300
What does "u" equal in this integral
∫(4x+1)^2 dx
u=4x+1
300
What is the extreme value theorem?
The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval.
300
What century did Issac Newton and Gottfried Wilhelm Leibniz develop calculus?
17th Century
400
Solve the limit
(4x^6)/(4x^8) as x approaches infinity
0
400
What rule uses this formula
(vu'-uv')/v^2
Quotient Rule
400
Solve the integral
∫(x)sin(x) dx
f(x)= -xcosx+sinx+c
400
What is the formula for chain rule?
f'(x)=f'(g(x))⋅g'(x)
400
Solve the integral
∫(cos^3(x))(sin(x)) dx
f(x)= ((-cos^4(x))/4)+c
500
Solve the limit
(4x-4)/(3x-3) as x approaches 1
4/3
500
Solve for the derivative
f(x)= (2x)((6x)^2)
f'(x)= 2x(72x)+((6x)^2)(2)
500
Solve the integral
∫(5x+7x)^2 dx
f(x)= 48x^3+c
500
What is the formula for L'Hopital Rule
500
Who was the first person to use the idea of limits?
Archimedes of Syracuse