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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    it is zero. use l'hopital's rule if it is not obvious that \[e^x\] grows much faster than \[x^e\]

  2. anonymous
    • 5 years ago
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    What is the "lim" part of the equation? What does it mean?

  3. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    oh i see

  6. anonymous
    • 5 years ago
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    i've never learned about limits, so do you mind explaining how you got zero?

  7. anonymous
    • 5 years ago
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    Does that mean that when x approaches infinity, the answer approaches zero?

  8. anonymous
    • 5 years ago
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    Yes right!

  9. anonymous
    • 5 years ago
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    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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