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Sikta Roy
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Asked: 2024-03-16T22:45:02+05:30 In:

Consider the following f(t)=0.01t2 g(t)=4t where 0<t<INFINITY Now, consider the following two statements (i)For some t>0,g(t)>f(t) (ii)There exists a T, such that f(t)>g(t) for all t>T? Which one of the following options is TRUE?

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Consider the following f(t)=0.01t2 g(t)=4t where 0<t<INFINITY Now, consider the following two statements (i)For some t>0,g(t)>f(t) (ii)There exists a T, such that f(t)>g(t) for all t>T? Which one of the following options is TRUE?
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  1. Sikta Roy
    Knowledge Contributor

    For (i) :

    f(1) = 0.01 and g(1) = 4

    So, there exists a t = 1, such that (i) is true.

    (ii) matches the definition of small oh notation

    Here, g(t) = o(f(t)) is true.

    So, f(t) > g(t) is always true for all t > T

    Hence, (ii) is also correct.

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