Derivatives
Integrals
Area/Volume
Limits
Misc.
100
A function that models the slope of the curve for all x-values for which it exists. This is the definition of what?
What is the definition of a derivative?
100
State the Integral Notation.
What is ∫_a^b f(x)dx
100
what is the format of integral that describes the volume made by a region whose cross sections when rotated around the x-axis were disks?
integral from a to b of pi (f(x)^2)dx
100
Name 3 conditions that must be met in order for a function to be continuous
What is F(a) must exist lim as x approaches a must extist limit value must = function value
100
State the formula for the Product Rule for Derivatives f(x)*g(x)
What is f'(x)g(x) +g'(x)f(x)
200
A line that passes through the curve at x=a and has a slope m=-1/F '(a). Name this type of line.
What is a Normal Line?
200
Evaluate the following from 0 to pi ∫ (sin x+2)dx
What is 2pi + 2?
200
A known __________ of A(x) can be used to find a volume of a solid. Fill in the blank..
What is a cross section?
200
In a graphic sense what does the limit as x approaches infinity find?
What are horizontal asymptotes?
200
Find any points where the graph fails to be differentiable and explain why 3√(5x+7)
What is y is not differentiable at x=-7/5 due to a vertical tangent
300
Find this equation's derivative: 4x^3 + 7x^2 + 2x + 3
What is the derivative of 12x^2 + 14x + x
300
State the Definite Integral Rules.
What is order of integration, zero, constant multiple, sum and difference and additivity.
300
This formula is used to find areas with more than one curve.
What is ∫_a to b of (f(x)-g(x) )dx?
300
Answer the following Limit Question: Lim x^2-3x-10/x^2-25 x->2
What is L=4/7
300
A function fails to be differentiable if it has a....
What is a discontinuity, corner, cusp or a vertical tangent
400
What is the limit definition of a derivative
Lim f(a+h)-f(a)/h h->0
400
This equation's derivative is: 25x^3 - 12x^2 + X. Find its intergral...
What is the derivative of 25x^4/4 - 4x^3 + x^2/2?
400
All cross sections to find a volume will be in circle form, the formula for the cross section is A(x)= A= pi r^2. Name this method..
What is the Disk Method?
400
what's the limit as x approaches infinity 7x^4+2x^7/4x^7
What is 1/2
400
Integrate the following equation ∫√(7x+9)dx
(2/21)(7x+9)^(3/2)+C
500
What is the derivative of inverse sine? inverse tangent? and inverse cosecant?
1/ √(a-x^2) ; 1/ (1+x^2) ; -1/ x √x^2-1
500
Integrate ∫((2x+1)^2)dx. from -1 to 3
What is 57 1/3?
500
Find the area enclosed by y=x^2 and the y-axis between [0,3] is revolved around the y-axis.
What is 9/2 pi
500
When plugging in value , you get limit is indeterminate. Name 2 ways you could find the limit
What are: Look for a solution graphically L'hospital's Rule
500
Find dy/dx and d^2y/dx^2 of the following equation y=3x^4-4x^(3/2)
What is 12x^3-6x^(1/2) and 36x^2-3x^(-1/2)
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