"S" words
This greek letter, which often represents summation,
\Sigma
What is "Sigma"?
2x
What is
x^2
Given n is a positive integer,
d/dx(x^n)=n\cdot x^{n-1}
What is the Power Rule of differentiation?
The function f with respect to the variable x is the function f' whose value at x is
f'(x)=lim_{h\rightarrow 0}(f(x+h)-f(x))/h
What is the Derivative?
This British mathematician is co-credited with a German mathematician with the co-discovery of Calculus.
Who is Sir Isaac Newton?
y=m\cdot x+b
What is "slope-intercept" form?
x
What is
1/2x^2
Given f(x) and g(x) are differentiable,
d/dx(f(x)+g(x))=d/dx(f(x))+d/dx(g(x))
What is the Summation Rule of Differentiation?
Assume f is defined in a neighborhood of c and let c and L be real numbers. The function f has limit L as x approaches c if given any positive number u, there is a positive number d such that for all x,
0<|x-c|<d\Rightarrow |f(x)-L|<u.
What is the definition of a Limit?
This German mathematician was co-credited with the discovery of Calculus.
Who is Gottfried Wilhelm Leibniz?
lim_{h\rightarrow0}(f(x+h)-f(x))/h
What is slope?
e^x
What is
e^x
Given f(x) and g(x) are differentiable functions and for g(x) not equal to zero,
d/dx(f(x)/g(x))=(f'(x)g(x)-f(x)g'(x))/(g(x)^2)
What is the Quotient Rule of Differentiation?
The line y=b is for the graph of a function y=f(x) if
lim_{x\rightarrow\infty}f(x)=b
What is a Horizontal Asymptote?
This mathematician proved the existence of these limits of sums and today these sums are named for him.
Who is Georg Riemann (1826-1866)?
Evaluate
d/dx(-cos(x))
What is sin(x)?
1/x
What is
ln(x)
\int_a^bk\cdot f(x)dx=k\int_a^bf(x)dx
What is the Constant Multiple Rule for Integration?
If y=f(x) is a non-negative and integrable over a closed interval [a,b], then this integral of f from a to be is
A=\int_a^bf(x)dx
What is Area Under a Curve (or Definite Integral)?
This Swiss mathematician has an irrational number named for him. This number solves (1+1/n)^n, as n goes to infinity.
Who is Leonhard Euler?
The area of this expression forms this geometric shape:
\int_{-5}^5\sqrt{25-x^2}dx
What is a "semi-circle"?
-x/\sqrt{25-x^2
What is
\sqrt{25-x^2}
For a<b<c and f(x),
\int_a^cf(x)dx=\int_a^bf(x)dx+\int_b^cf(x)dx
What is the Additivity Rule for Integration?
Let f be a function defined on a closed interval [a,b]. For any partition P of [a,b], let the numbers c_k chosen arbitrarily in the subintervals [x_{k-1},x_k] . If there exists a number I such that
lim_{||P||\rightarrow 0}\sum_{k=1}^nf(c_k)\Delta x_k=I
no matter how P and c_k s are chosen, then f is integrable on [a,b].
What is a Limit of a Riemann Sum (The Definite Integral)?
The dynamic approach to tangency was invented by this mathematician in 1629.
Who is Pierre de Fermat?