anonymous
  • anonymous
Evaluate the following: lim((x^e)/(e^x)), x -> infinity
Mathematics
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anonymous
  • anonymous
Evaluate the following: lim((x^e)/(e^x)), x -> infinity
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
it is zero. use l'hopital's rule if it is not obvious that \[e^x\] grows much faster than \[x^e\]
anonymous
  • anonymous
What is the "lim" part of the equation? What does it mean?
anonymous
  • 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

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anonymous
  • 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
anonymous
  • anonymous
oh i see
anonymous
  • anonymous
i've never learned about limits, so do you mind explaining how you got zero?
anonymous
  • anonymous
Does that mean that when x approaches infinity, the answer approaches zero?
anonymous
  • anonymous
Yes right!
anonymous
  • 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?

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