Pre-Calculus
A relationship between two quantities. One quantity is called input, the other is called output.
What is a function?
A value approached by y = f(x) as x approaches a given value.
What is a limit?
The instantaneous rate of change of
f(x)
when
x=a
What is
f'(a)?
int_a^bf(x)dx=F(x)+C
What is an indefinite integral?
(f(b)-f(a))/(b-a)
What is the formula for the average rate of change of f(x) on the interval [a, b]?
Power, polynomials, exponential, logarithmic, trigonometric
What is "families of functions"?
Numerical, Graphical, Algebraic or Analytical
What are three methods to find a limit?
d/dx[sin(x)]
What is
cos(x)?
int_a^bf(x)dx=F(b)-F(a) if f(x)=F'(x)
What is the Fundamental Theorem Of Calculus Part I?
f'(c)=(f(b)-f(a))/(b-a)
What is the Intermediate Value Theorem for Derivatives?
y - y1 = m(x - x1), y = mx + b, Ax +By - C = 0
What are the three equations of any line?
lim (x->a^-) f(x)
What is a left hand limit?
f'(x)=ncx^(n-1)
What is the derivative of a power function?
or
What is the derivative of
f(x)=cx^n
lim(n->00)sum_(i=1)^nf(x_i)/_\x
What is the limit definition of the definite integral?
(y2 - y1)/(x2 - x1)
What is the formula for slope of a line?
x=a
such that
lim(x->a^-)=+-00 or lim(x->a^+)=+-00
What is a vertical asymptote
lim(/_\x->0)(tan(x+/_\x)-tan(x))/(/_\x)
What is
sec^2(x)?
F(x)=x ln x - x + C
What is
int(ln x)dx?
Points where the graph of a function crosses the x-axis.
What are x-intercepts? or Zeros?
lim(h->0)(f(x+h)-f(x))/h
What is the limit definition of the derivative?
d/dt[v(t)]
What is acceleration? or What is
a(t)
int(v(t))dt
What is the position function? or What is
x(t)?