Limits
Volume
Integrals
Derivatives
100
What is a limit?
The limit of a function is the value that f(x) gets closer to as x approaches some number
100
What is Volume ?
The amount of space that a substance or object occupies.
100
What is a Integral ?
The integral is a mathematical object that can be interpreted as an area or a generalization of area.
100
What is the derivative ?
The Derivative is the instantaneous rate of change of a function with respect to one of its variables.
200
How can you find the limit ?
Direct Substitution , Factorization , Rationalization , and Reduction to Standard form.
200
What is the Formula for volume ?
200
What is the Definite Integral Rules
Constant multiple sum and difference and additivity , order of integration
200
What is the anti-derivative ?
An antiderivative of a function f(x) is a function whose derivative is equal to f(x).
300
Evaluate the Limit .
lim 5x^2-3x-1
x-> 4
Answer= 67
300
What is a cross section ?
A cross section of A(x) can be used to find a volume of a solid
300
Evaluate pi S (sin x +2)dx0
2pi+2
300
What is the formula to find the antiderivative.
400
Evaluate the limit.
lim 4y^5-5y^2-3y
y->-1
Answer = -6
400
What is the Disk Method.
The process of finding the volume of an object by dividing that object into many small cylinders/disks and then adding the volumes of these small disks together.
400
Find the Integral
S(5x^2-8x+5)dx
Answer = 5x^3/3 -4x^2+5x+C
400
What Theorem of Calculus uses the antiderivative ?
Fundamental Theorem of Calculus.
500
Evaluate the limit .
lim x^2-4x-4/x^2
x->2
Answer = -2
500
Find the volume of the closed region .
f(x)= 0 , x=y^2 , x=4 ( rotate this region across the x axis )
Answer = 8pi
500
Find the Integral
S(x^3/2 +2x+3)dx
Answer= 2x^5/2 +x^2+3x+C
500
Find the antiderivative of f(x)=2x-1 ?
Answer = f(x)= x^2-x+1