Question

Arrange the following functions in incresing asympotic order:
A. n${}^{1/3}$
B. $e^n$
C. $n^{7/4}$
D. n $lo{g}^9$ n
E. 1.000000${}^n$

• A. A, C, D,B, E
• B. A, C, D, E, B
• C. A, D, C, E, B
• D. D, A, C, E, B

Answer 1

The correct option is C A, D, C, E, B

A. n${}^{1/3}$ = (n)${}^{0.34}$
B. $e^n$ = (2.7)${}^n$
C. $n^{7/4}$ = ($n^{3/4}$) . ($n^1$) = ($n{)}^{1.7}$ =n($n^{3/4}$)
D. 1.000000${}^n$ = (1.0000001)${}^n$
So, (n)${}^{0.34}$ < n($lo{g}^{9}n$) < $n^{7/4}$ < (1.0000001)${}^n$ < (2.7)${}^n$
[A] < [D] < [C] < [E] < [B]