Question

What is the {eq}Theta

{/eq} – notation for the expression below? Select the correct answer.

{eq}(1/3)^n+n^6lg^2n+999n^6+3^{999}

{/eq}

Note that:

{eq}lgn=lg_2n \

lg^2n=(lg n)^2 \

A) Theta((1/3)^n) \

B) Theta(n^6lg^6n) \

C) Theta(n^6) \

D)Theta(3^{999} )

{/eq}

EXPERT ANSWER

The {eq}Theta

{/eq} notation for the expression {eq}(1/3)^n+n^6lg^2n+999n^6+3^{999}

{/eq}

is {eq}B) Theta(n^6lg^6n)

{/eq}

It’s not A because although {eq}(1/3)^n

{/eq} grows with *n*, it’s just a fraction, so it gets exponentially smaller with larger sizes of *n*.

It’s not C because it’s less than answer B. Remember the