Derivatives

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)