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Functions
Limits
Shortcuts to Differentiation
The Derivative
Jonas "Calc Man" Sieglaff
100
A function with the form 'y = mx + b'.
What is a linear function?
100
As a function approaches a value 'c', this number is as close to 'f(x)' whenever 'x' is sufficiently close (but not equal to) 'c'.
What is a limit?
100
[f(x) ± g(x)]' = f'(x) ± g'(x)
What is the sum and difference rule?
100
The instantaneous rate of change at a given point of a function.
What is a derivative?
100
An important concept that I found straightforward, useful, and interesting.
What are derivatives?
200
'P = P₀aᵗ'
What is the form for an exponential function?
200
The limit of 'f(x) = 2x + 3' as 'x' approaches 5.
What is 13?
200
(xⁿ)' = nxⁿ⁻¹
What is the power rule?
200
If the derivative represents speed, this represents acceleration.
What is the second derivative?
200
Something that was not completed regularly.
What is homework and notes?
300
This exponential function passes through points (0, 0) and (2, 3).
What is the function 'xˡᵒᵍ²⁽³⁾ - 1'?
300
The limit of 'f(x) = (2x + 1) / √x' as 'x' approaches 0.
What is ∞?
300
(aˣ)' = (ln a)aˣ
What is the derivative of an exponential function?
300
[D A I L Y D O U B L E] (d³y)/dx³
What is jerk?
300
Linearization.
What is my least favorite calculus topic?
400
This function is a ratio of two polynomials.
What is a rational function?
400
The limit of 'f(x) = 1 / mod(x, 1)' as 'x' approaches 2⁻.
What is 1?
400
(f ⋅ g)' = f' ⋅ g + f ⋅ g'
What is the product rule?
400
This would indicate on a graph that f'' is greater or equal to zero.
What is concave up?
400
Extra structure, walkthroughs and lecture from a talented individual.
What are some benefits of a dependent-study style course?
500
This is an example of a non-continuous function.
What is 'f(x) = tan(x)'
500
The limit of 'f(x) = (|x - 2|) / (x - 2)' as 'x' approaches 2⁻.
What is undefined?
500
[f(g(x))]' = f'(g(x)) ⋅ g'(x)
What is the chain rule?
500
| mod(x, 2) + 3x | is an example of this kind of function.
What is a non-differentiable function?
500
Matt Johnson.
Who is the greatest math teacher of all time?