Derivatives
A function that models the slope of the curve for all x-values for which it exists.
What is a derivative?
State the Integral Notation.
What is ∫_a^b f(x)dx
This method of finding volume of rotation is used when there is a hole or gap in the solid formed by rotation
What is the washer method
Name 3 things you can use to find limits
What is L'Hopital's Rule, Factor and Reduce, Conjugates, Substitution, Graphing, Tables
State the formula of the Product Rule for Derivatives
What is u'v + uv'
A line that passes through the curve at x=a and has a slope m=-1/F '(a).
What is a Normal Line?
Evaluate the following. ∫ (sin x+2)dx from 0 to pi
What is 2pi + 2?
A known __________ of A(x) can be used to find a volume of a solid. Fill in the blank..
What is a cross section?
State what is used to find a horizontal asymptote.
What is limit as x approaches infinity
Find any x-values 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 asymptote
Find this equation's derivative: 4x^3 + 7x^2 + 2x + 3
What is 12x^2 + 14x + 2
This equation's derivative is 1/x. Find its integral
What is ln |x| + c
This formula is used to find areas with more than one curve.
What is ∫_a^b(f(x)-g(x) )dx?
Answer the following Limit Question: Lim (x^2-3x-10)/(x^2-25) x->2
What is L=4/7
A function fails to be differentiable if it has a.... (name one)
What is a discontinuity, corner, cusp, or a vertical tangent/asymptote
What is the formula for Left Hand Derivatives?
Lim f(a+h)-f(a)/h h->0-
This equation's derivative is: 25x^3 - 12x^2 + X. Find its integral...
What is the derivative of (25/4)x^4 - 4x^3 + (1/2)x^2 + c?
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?
Answer the following Global Limit Equation (limit as x approaches infinity) (7x^4+2x^7)/(4x^7)
What is 1/2
Integrate the following equation ∫√(7x+9)dx
What is (2/21)(7x+9)^(3/2)+C
Name 3 Derivative rules
What is power, product, quotient, chain, implicit differentiation
Integrate ∫(-1)^(3) ((2x+1)^2)dx.
What is 57 1/3?
Find the volume found when the region enclosed by y=x^2 and the y-axis between [0,3] is revolved around the y-axis.
What is 81/2 pi
Name the 3 types of Discontinuities
What is Hole/Removable, Jump, Infinite
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)