Derivatives
Integral
Area/Vol.
Limits
Misc.
100
The definition of a derivative
What is lim h->0. ( f (a+h) - f (a))/h?
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
Find the limit x->0 ((x^3)+(cos(5x)/10,000)
What is 0.0001?
What is 1/10,000?
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: 5x^3 + 3x^2 + 2x + 6
What is the derivative of 15x^2 + 6x + 2?
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
What is the lim x->2 (x^2-3x-10/x^2-25)
What is 4/7?
300
A function fails to be differentiable if it has a.... (Name all that apply)
What is a discontinuity, corner, cusp or a vertical tangent
400
What is the formula for Left and Right Hand Derivatives?
What is Lim f(a+h)-f(a)/h h->0+ and h->0-?
400
This equation's derivative is: 25x^4 - 8x^3 + X. Find its intergral...
What is (25x^4)/5 - 2x^4 + (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
What is the lim x->16 ((4-√ x)/(16x-x^2))
What is 1/128?
400
Integrate the following equation ∫√(7x+9)dx
(2/21)(7x+9)^(3/2)+C
500
Name 7 of the 26 Derivative rules
1. The Definition of the Derivative.
2. The derivative of a constant is zero.
3. The derivative of a constant times a function.
4. The Power Rule (Variable raised to a constant).
5. The Sum Rule.
6. The Difference Rule.
7. The Product Rule.
8. The Quotient Rule.
9. The Chain Rule.
10. Another Form of the Chain Rule.
11. The Derivative of the Sine.
12. The Derivative of the Cosine.
13. The Derivative of the Tangent.
14. The Derivative of the Cotangent.
15. The Derivative of the Secant.
16. The Derivative of the Cosecant.
17. The Derivative of the Inverse Sine.
18. The Derivative of the Inverse Cosine.
19. The Derivative of the Inverse Tangent.
20. The Derivative of the Inverse Cotangent.
21. The Derivative of the Inverse Secant.
22. The Derivative of the Inverse Cosecant.
23. The Derivative of the Natural Log.
24. The Derivative of the log to base a.
25. The Derivative of e raised to a variable.
26. The Derivative of a constant raised to a variable.
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 the first and second derivative of the following equation y=3x^4-4x^(3/2)
What is 12x^3-6x^(1/2) and 48x^2-3x^(-1/2)?