$1.$ Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size n$,$ insertion sort runs in $4$n$2$ steps, while merge sort runs in $32$nlgn steps. For which values of n does insertion sort beat merge sort?

$2.$ Rewrite the INSERTION$-$SORT procedure to sort into nonincreasing instead of nondecreasing order.

$3.$ Express the function n$5/1000100$n$2100$n $+3$ in terms of $\backslash$Theta $-$notation.

$4.$ Show that for any real constants a and b$,$ where b $>0,($n $+$ a$)$b $=\backslash$Theta $($nb$).$

$5.$ YesorNo$-$is$2$n$+1=$O$(2$n$)?$Why?

$6.$ Yes or No $-$ is $22$n $=$ O$(2$n$)?$ Why?