some notation commonly seen in calculus 1 courses. Includes the symbol, it's meaning, and sample usage.

1. Math 170 Notation
Tyler Murphy
October 8, 2014
In calculus, there is a lot of notation. This document is to help you make sense of it
and see how it's used.
Symbol Meaning Sample Usage
Summation
Pn
k=1 k2 =
1
2
n(n + 1)
limx!1 f(x) the limit of f(x) as x approaches in

2. nty limx!1
3x
5x
=
3
5
limx!a f(x) the limit of f(x) as x approaches some number a limx!0
3x
5x
=
3
5
f0(x); f0,
d
dx
f(x) the derviative of: f(x); f

3. nd f0(x) for f(x) = x2
y0; dy
dx The derivative of y with respect to x
d
dx
(xy) = y + dy
dx
f00(x); f00; d2
dxf(x) the second derivative of f f(x) = x2:f 00(x) = 2
dn
dx (f(x)) the nth derivative of f(x)
d10
dx
x10 = 10!
@u
@t
the partial derivative of u with respect to t.
@u
@t
= h2
@2u
@x2 +
@2u
@y2 +
@2u
@z2
R b
a the de

4. nite integral from a to b
R 2
1 (x3 4x2 R + 1) dx
the integral (also called the antiderivative)
R
x2 = x3
3 + C
Lastly, here are some key ideas to understanding what derivatives are and some termi-
nology associated with this class.
1

5. The derivative is a rate of change - basic terminology
The derivative at a point is the slope of the tangent line at that point.
It measures how sensitive a dependent variable to small changes in an indepen-
dent variable.
ratio of output change to input change
marginal cost - cost of producing 1 additional unit
velocity is derviative of position
acceleration is derivative of velocity
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