Covers Chapter $6$ Sections $7\mathrm{.}1-7\mathrm{.}3$

PROBLEM $1$

Solve the following $4$ problems on a separate sheet of paper:

a$.$ What is the Big$-$Theta of $5n+12?$

b$.$ What is the Big$-$Theta of $2n^3+3n?$

c$.$ What is the Big$-$Theta of $60n^2+4512?$

d$.$ What is the Big$-$Theta of $12?$

e$.$ What is the Big$-$Theta of$.nlo{g}_4(3n)?$

PROBLEM $2$

Using the definition of Big$-$Theta, prove that $f(n)$ is in $(n)$ when $f(n)=3n+344$

PROBLEM $3$

Using the definition of Big$-$Theta, prove in which Big$-$Theta $f(n)$ is a member when $f(n)=3n^3+4n$

PROBEM $4$

On the graph below, draw an estimate of the $f(n)$ line, a line for $O(g(n)),(g(n)),$ and $n_0$ when $f(n)=4n+4.$ Additionally, add the labels Big Data, No Data, Fast, and Slow.