tilde approximations required for the below

By user3766874

Can you please tell me along with the explanations how to calculate tilde approximations for the below functions.

a. 1 + 1/N
b. (1 + 1/N )(1 + 2/N )
c. lg(2N )/lg N
d. lg(N^2 + 1) / lg N
e. N^100 / 2^N

Thank you.

Source: Stack Overflow


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