Evaluate the following: lim((x^e)/(e^x)), x - infinity

Question

Evaluate the following: lim((x^e)/(e^x)), x -> infinity

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

oh i see

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Yes right!

anonymous · Answer

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?