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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
This curve is closest to the x-axis when finding areas with more than one curve.
What is a minor curve?
100
Name 3 of the rules to find limits
What is Difference Rule, Constant Multiple Rule, Product Rule, Power Rule, Quotient Rule
100
State the formula of the Power Rule for Derivatives
What is A'b + B'a
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. pi ∫ (sin x+2)dx 0
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
State the definiton of a global limit.
What is limits involving infinity
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^b(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 formula for Left and Right Hand Derivatives?
Lim f(a+h)-f(a)/h h->0+ and 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
Answer the following Global Limit Equation 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
Name 8 of the 17 Derivative rules
Answer will vary...
500
Integrate ∫(-1)^(3) ((2x+1)^2)dx.
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
Name the 4 types of Discountinuties
What is Hole, Jump, Infinity, Oscillating
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 48x^2-3x^(-1/2)