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Derivatives
Integrals
Area/Volume
Limits
Misc.
100

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?

100

You must write this when finding the indefinite integral of a function

What is +c?

100

Name at least one method to approximate the area of a region.

What is Riemann sum, trapezoidal sum?

100

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?

100

This type of polynomial is used to approximate a function centered at a point

What is Taylor polynomial?

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 perpendicular line?

200

Evaluate the following 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
The value of a function as x approaches infinity or -infinity

What is a horizontal asymptote, or what is a limit at infinity?

200

This is used to estimate the error of a power series

What is Lagrange error bound?

300

Find this equation's derivative: 4x^3 + 7x^2 + 2x + 3

What is the derivative of 12x^2 + 14x + 2

300

This is a method to approximate the solution of a differential equation

What is Euler's method?

300
This formula is used to find areas with more than one curve.
What is ∫_a^b(f(x)-g(x) )dx?
300

Evaluate Lim (x^2-3x-4)/(x - 4) x->4

What is 5?

300

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?

400

What is the limit definition of the derivative at a point?

Lim f(a+h)-f(a)/h h->0

400

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?

400

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?

400

lim (7x^4+2x^7)/4x^7 x->infinity

What is 0?

400

The type of curve where x and y are in terms of a third parameter

What is a parametric curve?

500

Name 8 of the 17 Derivative rules

Answer will vary...

500

Integrate ∫2x/(3x^2 + 6)dx.

What is 1/3 ln(3x^2 + 6) + c

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
Evaluate lim sin(4x)/2x x->0

What is 8?

500

f is a vector valued function, defined by f(t) = <3t + t^2, 6t - t^3>. Find f'(2)

What is <7, -6>?