Derivatives
Three derivative rules.
What is (three of the following):
- Power Rule
- The Product Rule
- Quotient Rule
- The Chain Rule
The integral of this function?
f'(x)= 3x2+5x-2
What is
y= x3+ 5/2x2-2x+C ?
(No points if you forgot the +C)
The mathematician that came up with this rule.
If the limit as x approaches c of "f(x) over g(x)" equals zero over zero, then it equals the limit as x approaches c of "f'(x) over g'(x)"
Who is Guillaume de L'Hôpital?
(L'Hospital is acceptable)
Five series test.
What are (five of the following):
- Absolute Convergence
- Divergence Test
- Integral Test
- Alternating Series Test
- Ratio Test
- Nth Term Test
- Geometric Series Convergence
- P-Series Test
- Taylor Series Convergence
- Root Test
Two theorems of Calculus.
What are (two of the following):
- Intermediate Value Theorem
- Extreme Value Theorem
- Mean Value Theorem
This can be found when setting the second derivative of a function equal to zero.
What is...
The point of inflection?
The anti-derivative of velocity.
What is POSITION?
The mathematician that came up with a way to approximate the area under a function using rectangles.
Who is Bernhard Riemann?
(Reimann is acceptable)
The letter that represents the independent variable in parametric equations.
What is t?
3 types of discontinuities.
What are (3 of the following):
The derivative of this function.
y= (x3)(3x+9)
*HINT- Use the product rule
What is:
f'(x)= 12x3+27x2 ?
This is represented on the graph of the integral from the original function.
What is the AREA?
The mathematician that claims series of a function about x=0.
Who is Brook Taylor?
(Taylor is acceptable)
The formulas to convert a polar equation r to parametric functions x and y.
What are
x = rcosθ
y = rsinθ?
This is represented by a factorial.
What is the number of ways n objects can be arranged in order?
The derivative of velocity with respect to time.
What is the ACCELERATION?
This is how you find the new bounds of an integral after u-sub.
What is plug the original bounds into the function of u?
The mathematician that claims the error bound by a Taylor series.
Who is Colin Maclaurin?
(Maclaurin is acceptable)
Given the velocity vector <t3 +2t, 4t2 - t>, the speed of the particle at t = 1.
What is 3√2?
The role that Mr. Magnus played in his high school musical.
Hint: The Wizard of Oz
What is the Mayor of Munchkinland?
This is represented by the graph of a derivative from a function.
What is the slope of the tangent lines?
This is when you have to use integration by parts.
What is:
The integration by parts is used when the simple process of integration is not possible. If there are two functions and a product between them, we can take the integration between parts formula.
The two mathematicians that invented Calculus.
Who are Issac Newton and Gottfried Wilhelm Leibniz?
(Last names are acceptable)
The function that this Maclaurin series originates from.
1 + x + x2 + x3 + ...
What is 1/(1 - x)?
The theorem that represents:
If h(x) <= g(x) <= f(x) when x is near a, except possibly at a, and the limit as x approaches a of f(x) equals the limit as x approaches a of h(x) equals L, then the limit as x approaches a of g(x) equals L.
What is squeeze/sandwich theorem?