Derivatives
A function that gives the slope of a curve for all x-values for which it exists. This is the definition of what?
What is the definition of a derivative?
You must write this when finding the indefinite integral of a function
What is +c?
Name at least one method to approximate the area of a region.
What is Riemann sum, trapezoidal sum?
The limit of a function does not exist at a point in these situations.
What is a non-removable discontinuity (jump or vertical asymptote) or when a function oscillates?
This type of polynomial is used to approximate a function centered at a point
What is Taylor polynomial?
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 perpendicular line?
Evaluate the following 0 to pi∫ (sin x+2)dx
What is 2pi + 2?
What is a horizontal asymptote, or what is a limit at infinity?
This is used to estimate the error of a power series
What is Lagrange error bound?
Find this equation's derivative: 4x^3 + 7x^2 + 2x + 3
What is the derivative of 12x^2 + 14x + 2
This is a method to approximate the solution of a differential equation
What is Euler's method?
Evaluate Lim (x^2-3x-4)/(x - 4) x->4
What is 5?
Name at least three tests that can only be used for a series with positive terms.
What is integral test, p-series test, limit comparison and direct comparison test?
What is the limit definition of the derivative at a point?
Lim f(a+h)-f(a)/h h->0
The derivative of a function is: 25x^3 - 12x^2 + x. Find the function.
What is the derivative of 25x^4/4 - 4x^3 + x^2/2 + c?
We use this method to find the volume of a plane region revolved about an axis of revolution (AoR) if there is a gap between the region and the AoR.
What is the washer method?
lim (7x^4+2x^7)/4x^7 x->infinity
What is 0?
The type of curve where x and y are in terms of a third parameter
What is a parametric curve?
Name 8 of the 17 Derivative rules
Answer will vary...
Integrate ∫2x/(3x^2 + 6)dx.
What is 1/3 ln(3x^2 + 6) + c
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
What is 8?
f is a vector valued function, defined by f(t) = <3t + t^2, 6t - t^3>. Find f'(2)
What is <7, -6>?