7. We say a sequence {an} grows slower than {bn} if lim An = 0 NX...

 

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7. We say a sequence {an} grows slower than {bn} if lim An = 0 NX bn and then we write {an} < {bn}. The following describes the growth rates of many standard sequences {(Inn)} < < {n} < {n (lnn)} < {b"} < {n!} {n"} Here p, q> 0 and b > 0. Use L'Hospital's rule to check the following limits which illustrate several of the above growth rates. In n (a) lim NX Inn (b) lim nx 0.0001 3 n +11 (c) lim NYX 3n n ln n (d) lim nx n.1 +17n + 2 7. We say a sequence {an} grows slower than {bn} if lim An = 0 NX bn and then we write {an} < {bn}. The following describes the growth rates of many standard sequences {(Inn)} < < {n} < {n (lnn)} < {b"} < {n!} {n"} Here p, q> 0 and b > 0. Use L'Hospital's rule to check the following limits which illustrate several of the above growth rates. In n (a) lim NX Inn (b) lim nx 0.0001 3 n +11 (c) lim NYX 3n n ln n (d) lim nx n.1 +17n + 2