The document contains mathematical equations for: 1) Simplifying a fraction involving addition and multiplication. 2) Describing a polynomial function in terms of coefficients and exponents. 3) Defining the limit as n approaches infinity of 1 plus 1/n all raised to the nth power. 4) Computing the sample variance of a data set as the average squared deviation from the mean. 5) Computing the integral of 1 minus x squared from -1 to 1, which is a definition of pi over 2.

1. 2 3 2×43×3 17
 = =
3 4 3×4 12
f  x =a n x nan−1 x n−1⋯a1 xa0
n
f  x= ∑ ar xr
r =0
n
e=lim 1
n ∞
  1
n
N
=
 1
N
∑  xi −x 2
i=1
1
=2⋅  1−x 2 dx
∫
−1