Question

find the limit as x approaches infinity of x^20/e^x

also written as : \[\lim_{x \rightarrow \infty} x ^{20}/e ^{x}\]

a) 0/0
b)1
c)0
d)1/e

Answer 1

e^x will dominate x^20, so you will have large number divided by infinity which is like....

4/10,000,000 which is essentially zero

Answer 2

so it would be c which is 0 and not a which is 0/0

Answer 3

If you do L'Hospital's Rule 20 times, you will get 20! in the nummerator and e^x in the denominator, so the limit is zero
\[
\lim_{x->\infty}\frac {20!}{e^x}=0
\]

Answer 4

It would be c, remember dividing anything by zero, even zero, is undefined.