## anonymous 5 years ago Evaluate the following: lim((x^e)/(e^x)), x -> infinity

1. anonymous

it is zero. use l'hopital's rule if it is not obvious that $e^x$ grows much faster than $x^e$

2. anonymous

What is the "lim" part of the equation? What does it mean?

3. anonymous

ah you are trying to see what number this ratio approaches as x gets large. as x goes to infinity the denominator is much bigger than the numerator so the limit is 0

4. anonymous

imagine for a second that e=3 which it does not but e is less than 3. 10^3 = 1000 but e^10=22026 . this difference in magnitude grows as x gets larger. for example 1000^3=10^9 but e^1000 will overflow your calculator

5. anonymous

oh i see

6. anonymous

i've never learned about limits, so do you mind explaining how you got zero?

7. anonymous

Does that mean that when x approaches infinity, the answer approaches zero?

8. anonymous

Yes right!

9. anonymous

Okay One of the problems is has $\lim_{x \rightarrow 3}$ but instead of an arrow, there's the letter R in a circle. Is that a typing error by my teacher?