BiM$122$ Discrete Computational Structures

HW $2$

$(50$ pts$)$ Find the least integer $n$ such that $f(x)$ is $O(x^n)$ for each of these functions.

a$)f(x)=2x^3+x^{2}logx$

b$)f(x)=3x^3+(logx{)}^4$

c$)f(x)=\frac{x^4+x^2+1}{x^3+1}$

d$)f(x)=\frac{x^4+5logx}{x^4+1}$

$(50$ pt$)$ Find the number of vertices, the number of edges, and the degree of each vertex

in the given undirected graph.