Methods Flash Cards

Beschreibung

Karteikarten am Methods Flash Cards, erstellt von Hannah Williams am 13/11/2017.
Hannah Williams
Karteikarten von Hannah Williams, aktualisiert more than 1 year ago
Hannah Williams
Erstellt von Hannah Williams vor mehr als 6 Jahre
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Zusammenfassung der Ressource

Frage Antworten
Quadratic formula
Closed interval
Open interval
Infinite
Equation of a straight line
General equation of a conic
Ellipse equation in standard form
Ellipse equation in parametric form
Hyperbola equation in standard form
Hyperbola equation in parametric form
Parabola in standard form
Parabola in hyperbolic form
Definition of the domain What goes into the function, the x values
Definition of the codomain What may possibly come out of the function
Definition of the range What actually comes out of a function, the y values
Definition of a one-to-one function Every element of the range corresponds to one element of the domain
Definition of an even function Symmetrical about the y-axis
Definition of an odd function Rotational symmetry about the origin
Definition of a periodic function Graph repeats itself every T
Monotonically increasing
Monotonically decreasing
Composite function
Inverse function where f(x) is one-to-one
Conditions for a function f(x) to be continuous at c
nth term of an arithmetic sequence
nth term of a geometric sequence
Sum/difference rule
Product rule
Quotient rule
Sandwich theorem
Sum of n terms of an arithmetic series
Sum to n terms of a geometric series
Sum to infinity of a geometric series
Properties of convergent series
Divergence test
Comparison test
Ratio test
Leibniz' theorem
Absolute convergence and it is said to converge absolutely.
Formal definition of a derivative
Product rule
Quotient rule
Chain rule
Second derivative chain rule
Leibniz rule for repeated differentiation of products
The linearization of f(x) at x=a
Extreme value theorem of continuous functions If f(x) is continuous at every point on [a,b] then f takes both its maximum and minimum values on this interval.
Concave function f f is concave if any chord joining two points lies above the graph
Convex function f f is convex is any chord joining two points lies below the graph
Point of inflexion then x is a point of inflexion
L'Hôpital's rule (for functions) If f(a)=g(a)=0 (or f(a)=g(a)=∞), and we can evaluate f'(a) and g'(a), then
Intermediate Value Theorem A function f(x) that is continuous at all x∈[a,b] takes on every value between f(a) and f(b)
Rolle's Theorem Suppose that f(x) is continuous at all x∈[a,b] and it is differentiable at all x∈(a,b), and f(a)=f(b), then there is at least one value c∈(a,b) such that f'(c)=0
The Mean Value Theorem Suppose that f(x) is continuous at all x∈[a,b], it is differentiable at all x∈(a,b) then there is at least one c∈(a,b) such that
Constant Difference Theorem
Maclaurin series
Taylor series
Remainder term, Taylor's theorem
Remainder estimation where M and R are positive constants
Scalar product
Vector product
Equation of a line (vectors)
Equation of a plane (vectors)
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