Time Complexity

Show that $n^2+50n=O(n^2).$

Show that $n^2+n^2+n^2=3n^2=O(n^3).$

The running time complexity of a linear time

algorithm is given as

$($a$)0(1)$

$($b$)0(n)$

$($c$)O(nlogn)$

$($d$)O(n^2)$

Which notation comprises a set of all functions

$h(n)$ that are greater than or equal to $cg(n)$ for all

values of $n{n}_0?$

$($a$)$ Omega notation

$($b$)$ Big O notation

$($c$)$ Small o notation

$($d$)$ Theta Notation

$540n^2+10$

$(n^2).$