The house-numbers on a certain street go from 1 11 to 88 8888. The function B ( n ) B(n)B, left parenthesis, n, right parenthesis models the type of the building whose number is n nn according to the following key: Building type Function output Residential building 0 00 Commercial building 1 11 Government building 2 22 Other 3 33 Which number type is more appropriate for the domain of B BB?

Interpreting as: B ( n ) B(n)B

Assuming multiplication
Input:
B n (B(n) B)

Result:
B^2 n B(n)

Series expansion at n = 0:
B^2 B(0) n + B^2 n^2 B'(0) + 1/2 B^2 n^3 B''(0) + 1/6 B^2 B^(3)(0) n^4 + 1/24 B^2 B^(4)(0) n^5 + O(n^6)
(Taylor series)

Big‐O notation
Definite integral over a square of edge length 2 L:
integral_(-L)^L integral_(-L)^L B^2 n B(n) dn dB = 2/3 L^3 n B(n)

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