algorithms

Question

Answer 1

Given,

f(n)=n

g(n)=n^{(1+sin n)}

the value of sin n will be between -1 and 1 so g(n) will be between n^(1-1)=1 and n¹⁺¹=n², depending on the value of n

So one cant bound the other for large value of n,

Hence answer is  D

black line is f(n) and blue curve is g(n)

Heres the link for the graph: http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4IiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjowLCJlcSI6InheKDErc2luKHgpKSIsImNvbG9yIjoiIzVEMThCRCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0xNjIuNDk5OTk5OTk5OTk5NzIiLCIxNjIuNDk5OTk5OTk5OTk5NzIiLCItOTkuOTk5OTk5OTk5OTk5ODIiLCI5OS45OTk5OTk5OTk5OTk4MiJdfV0-

Comments

I still  not understand properly brother as you said g(n) will be in b/w n^0 and n^2 then why it can't be both A  and C ,Please make me right whatever I am interpreting wrong.