Thursday

March 5, 2015

March 5, 2015

Posted by **lola** on Wednesday, February 1, 2012 at 4:55pm.

(n^100)/(e^n)

...If you do L'Hop. Rule it would take forever, right? You would always get an (e^n) at the bottom and will have to use the L'Hop. rule 100 times to find the limit...100*n^99, 9900n^98, and etc.

Is there a shortcut to find the limit?

Or, am I doing something way wrong?

calc - Reiny, Wednesday, February 1, 2012 at 12:06pm

You didn't say what the aprroach value is for n

is n---> 0 ?

lim n^100/e^n)

= lim (100n^99)/(e^n)

= lim (9900n^98) / e^n

= ...

= lim (huge n^1)/e^n

= lim (more huge )/e^n

= lim (0/e^n)

= 0/1

= 0

calc - lola, Wednesday, February 1, 2012 at 12:29pm

what if n approaches infinity?

- calc -
**Steve**, Wednesday, February 1, 2012 at 5:26pmThis shows that any polynomial, no matter how high the degree, grows more slowly than any exponential function of a base >1.

Repeated application of L’Hopital’s Rule just reduces the degree of the numerator by 1, and when you get to a constant, one more application reduces the numerator to ZERO. The denominator is still e^x.

- calc -
**lola**, Wednesday, February 1, 2012 at 6:06pmso the limit is zero

- calc -
**lola**, Wednesday, February 1, 2012 at 6:25pmis the limit zero?

**Answer this Question**

**Related Questions**

calc - Use L’Hopital’s rule to find the limit of this sequence (n^100)/(e^n) ......

calc2 - Use L’Hopital’s rule to find the limit of this sequence (n^100)/(e^n...

limit calc question - 2 questions!!! 1. Limit X approaching A (X^1/3-a^1/3)/ x-a...

calculus, limits, l'hopital - Using l'hopital's rule, find the limit as x ...

calculus, limits, l'hopital - Using l'hopital's rule, find the limit as x ...

Calculus - How would I solve the limit for this sequence. [n^(2)]*[1-cos(2.4/n...

Calclulus - L'Hopital's Rule - Evaluate the limit as x -> Infinity [5x-sqrt(...

Calculus - Find the limit as x approaches infinity of (lnx)^(1/x). This unit is ...

Calculus - find the limit. use L'Hopital's Rule if necessary. lim (x^2+3x+2)/(x^...

Calculus - Using L'Hopital's Rule, find the limit: lim x->0+ (as x approaches...