Question

Ranking the following functions in increasing order of (asymptotic) magnitude Drag and drop to order 1 = A 100! 2 B n 100 3 с log1001 = D 100n 5 nlog(100) 100" Activate Window

Answer 1

Take logarithm on all the functions

A)log(100!)

B)100log(n)

C)log()

log100n

D)log(100n)=log(100)+log(n)

E)log(nlog(100n))= log(n)+ log(log(100n)

F)nlog(100)

For example

We if take n=$100^{200}$

then

A=157.9

B=$100^{200}$*log($100^{200}$)= $100^{200}$ *400

C=log(200)

D=log(100*$100^{200}$)= log($100^{201}$) =log(402)

E=log($100^{200}$*log(402)) = 400+log(log(402))

F=$100^{200}$*2

Here 100! is just a constant

I just took an example of $100^{200}$ to explain how n varies among B C D E F

But in A there is no n hence it will last because when we take very very large numbers then log of those value may be greater than 100! .

Hence the order will be

F>B>E>D>C>A

or

A<C<D<E<B<F