Greeks and Romans
This greek symbol represents the ratio of a circles circumference to its diameter.
What is
pi
Given any positive number u, there exists an d such that for all x,
0<|x-c|<d \Rightarrow |f(x)-L|<u
What is the Limit?
If a function f has a local maximum value or a local minimum value at an interior point of the domain and if f' exists at c, then
f'(c)=0
What is the Local Extreme Values Theorem?
Power rule
d/dx(x^n)=n\cdot x^{n-1}
Sir Isaac Newton (1642-1727)
What is recognized for the discovery of calculus (among other things).
This greek symbols represent the change in a variable.
What is
Delta
Given f(a) exists and
\lim_{x\rightarrowa}f(x)=f(a)
What is continuity?
If f is continuous on [a,b], then at some point c in [a,b],
f(c)=1/(b-a)\int_a^bf(x)dx
What is the Mean Value Theorem for Definite Integrals?
Chain Rule
What is
dy/dx=dy/(du)\cdot (du)/dx
Benjamin Franklin (1706-1790)
What is a polymath and inventor?
This is a Roman symbol to represent the change as the change goes infinitesimally small.
What is "d"?
(y_2-y_1)/(x_2-x_1)
What is slope?
If g(x) <f(x)<h(x) for all x in an interval about c and
\lim_{x\rightarrow c}g(x)=\lim_{x\rightarrow c}h(x)=L
then
\lim_{x\rightarrow c}f(x)=L
What is the Sandwich Theorem?
Quotient Rule
d/dx(f(x)/g(x))=(f'(x)g(x)-f(x)g'(x))/(g(x)^2)
Gottfried Wilhelm Leibniz (1646-1716)
Who made a breakthrough in his notebook on November 11, 1675 when he used integral calculus to estimate the area under a curve? Leibniz is recognized as a co-discoverer of calculus. Newton claimed Leibniz plagiarized his work.
This greek symbol is used to denote the summation operator.
What is
Sigma
\lim_{h\rightarrow0}(f(x+h)-f(x))/h
What is the derivative?
If f is continuous on [a,b], then
F(x)=\int_a^xf(t)dt
has a derivative at every point x in [a,b] and
(dF)/dx=d/dx\int_a^xf(t)dt=f(x)
What is the Fundamental Theorem of Calculus, part 1?
Jump discontinuity
What is a discontinuity at a point such that the limit exists at that point; however; the limit does not equal the value of the function at that point?
Pierre de Fermat (1601-1665)
What is a method for determining the slope of the tangent line?
This is the Roman symbol to indicate sum as the change goes infinitesimally small.
What is
\int
\int_a^bf(x)dx
What is the definite integral?
If f is continuous at every point of [a,b] and if F is any antiderivative of f on [a,b], then
\int_a^bf(x)dx=F(b)-F(a).
What is the Fundamental Theorem of Calculus, part 2?
Left-hand limit
What is
\lim_{x\rightarrow a^-}f(x)
Georg Riemann (1826-1866)
What is proved the existence of Definite Integrals (a Riemann sum as the partition norm goes to zero)?