Memorized Derivatives/integrals
The derivative of 4x^3 + 5x^2 - x + 5 is this polynomial
What is 12x^2 +10x - 1?
The formula for work is represented by this formula (when force is constant)
What is Work = FD (Force x Displacement)?
This technique is to replace a function with a letter to simplify the integral.
What is u-substitution?
This is the correct taylor series for ex
What is 1 + x + (x^2)/2! + (x^3)/3!?
When f(x) changes from (+) to (-) at a point, the point is considered one of these
What is a local maximum?
This is the correct derivative of csc(x)
What is -csc(x)cot(x)?
If a function is continuous on [a,b], and differentiable on (a,b), then there must be a value c for which f'(c)= {f(b)-f(a)}/{b-a}, by this calculus theorem?
What is the Mean Value Theorem (MVT)?
This technique is used when there is a factorable denominator, and splits up the denominator to make the integral easier to do.
What is Partial Fraction Decomposition?
Daily Double (wager as many points as you would like, within the amount you have already, unless you have under 1000, in which case 1000 points is the maximum wager)
This is the radius of convergence for the little 4 taylor series
What is 1?
This is a place on a graph where concavity changes
What is an inflection point?
This is the correct integral for the function tan(x)
What is -ln|cos(x)| + C?
P = M/(1 + Ce-kt) is a formula for this function
What is the Logistic function?
This integration technique is used when there is something noticeable in the integral that can be used to easily do the integral.
What is The "Hey, I recognize that" technique?
This function is represented by the taylor series:
x - (x^3)/3 + (x^5)/5 - (x^7)/7
What is tan-1(x)
These are places on the graph where local maximums and minimums can be
What are critical points and endpoints?
This is the correct derivative of u/v
What is (vu'-uv')/v2?
This is the formula for this Chapter 10 concept:
error < max |f(n+1)(x)| x ((b-c)(n+1))/(n+1)!
c<x<b
What is the LaGrange Error Bound?
This integration technique is used when there are two functions that are not derivatives or integrals of each other, requiring each of them to be substituted with a letter.
What is Integration by Parts?
1 - (x^2)/2! + (x^4)/4! - (x^6)/6! is the correct taylor series for this function
What is cos(x)?
This is the "classic" related rates problem
What is the ladder problem?
This is the correct integral for the function 1/x
What is ln|x| + C?
This formula is used to show speed using parametrics
What is [(x'(t))2 + (y'(t))2]1/2?
This technique is used when there is a complex function inside an integral that is easily rewritten to make it much easier to integrate
What is Algebraic Simplification?
x - (x^2)/2 + (x^3)/3 - (x^4)/4 is the correct taylor series for this function
What is ln(1+x)
The Second Derivative Test is used for this purpose
What is to check the concavity of the function at critical points?