Edit the answer, Option C is correct.

Dark Mode

1,108 views

1 vote

Consider two functions of time $(t),$

$$

\begin{gathered}

f(t)=0.01 t^2 \\

g(t)=4 t

\end{gathered}

$$

where $0<t<\infty.$

Now consider the following two statements:

- For some $t>0, g(t)>f(t)$.
- There exists a $T,$ such that $f(t)>g(t)$ for all $t>T$.

Which one of the following options is $\text{TRUE}?$

- only (i) is correct
- only (ii) is correct
- both (i) and (ii) are correct
- neither (i) nor (ii) is correct

3 votes

Given,

$f(t)=0.01t^{2}$

$g(t)=4t$

and $0< t< \infty$

for option $(i)$,

take $t=1$,Now,

$f(1)=0.01$

$g(1)=4$,

So, here exists some $t$ ,t=1 , for which $g(t)>f(t).$ So $(i)$ is true .

for option $(ii)$,There exists some $ T=1000$(say) .Now any $t>T$ , $f(t)>g(t)$ .

So option (II) is also true .

This question is nothing but Big oh definition .

$g(t)\leq cf(t)$ for all $t>T$ and $c>0$ .

https://en.wikipedia.org/wiki/Big_O_notation

So correct option is (C) .