Calculus Terms
Limits
Integrals
Derivatives
Series
100
Rule that states (f(x)g(x))' = f'(x)g(x) + g'(x)f(x)
What is the Power Rule
100
Test to find if a series is absolutely convergent or not
What is the Ratio Test
100
Mathematician whose eponymous sum is often used to define definite integration
Who is Riemann
100
Term for a function for which the derivative exists at each point in the domain
What is differentiable
100
Series centered around x=0
What is the Maclaurin Series
200
Collective term for maxima and minima of a function
What is an extrema
200
Points where a function isn't continuous but can become continuous with a small adjustment
What are removable discontinuities
200
Integration by substitution
What is u-substitution
200
These locations of the derivative are (some of the) critical points of the function
What are x-intercepts
200
Test to find if series diverges
What is the nth term test
300
Theorem: If g(x)≤f(x)≤h(x) and lim(x→a) g(x) = lim(x→a) h(x) = L, then lim(x→a) f(x) = L
What is the Squeeze or Sandwich Theorem
300
Rule where you differentiate the numerator and differentiate the denominator and then take the limit
What is L'Hopital's Rule
300
Additive to indefinite integral solutions
What is C
300
Rule where you differentiate the numerator and differentiate the denominator and then take the limit
What is L'Hopital's Rule
300
A method used to test infinite series of non-negative terms for convergence
What is the Integral Test
400
Theorem that establishes the connection between derivatives and integrals
What is the Fundamental Theorem of Calculus
400
A limit being different from the left than it is from the right
What is a non existent limit (the limit does not exist).
400
What you find integrating the difference between two functions
What is the area between curves
400
Can be mathematically expressed as s''(t)
What is acceleration
400
Diverges if |r|≥1, Converges to (a/1-r) if |r|≤1
What is the Geometric Series
500
Process that deals with finding the 'best' value under certain constraints
What is Optimization
500
lim sin(1/x) for example x→0
What is a non existent limit
500
Formula: ∫udv=uv-∫vdu
What is integration by parts
500
Theorem that states for certain functions, f(b) - f(a) = f'(c)(b - a) for some c∈(a,b)
What is the Mean Value Theorem
500
A series which represents a function as a polynomial that goes on forever and has no highest power of x
What is a power series
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