is these true or false ?and explain why
a)if f(n)=O(g(n)) then 2^(f(n)=O(2^(g(n)))... please solve without lim
b)if f(n)=o(g(n)) then 2^(f(n)=o(2^(g(n)))... please solve without lim
FALSE
If f(n) = O(g(n)),
2^(f(n)) not equal to O(2^g(n)))
Let, f(n) = 2log n and g(n) = log n
(Assume log is to the base 2)
We know, 2log n <= c(log n) therefore f(n) = O(g(n))
2^(f(n)) = 2^log n^2 = n^2
2^(g(n)) = 2^log n = n
We know that
n^2 is not O(n)
Therefore, 2^(f(n)) not equal to O(2^g(n)))
is these true or false ?and explain why a)if f(n)=O(g(n)) then 2^(f(n)=O(2^(g(n)))... please solve without lim...
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Please answer true or false. If false, explain why.