Find the limit of (b^n+1+ a^n+1)/(b^n + a^n) as n goes to infinity

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In this video we find the limit of (b^n+1+ a^n+1)/ b^n + a^n where a is greater than b!
  1. Alex Li
  2. lhopitals
  3. lhopitals rule
  4. sum of n numbers
  5. limit
  6. calculus limits
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Комментарии
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Actually this is only true if a ≠ 0. Otherwise the limit is equal to b.

theimmux
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Assuming that a>0 and b>0 the limit is a.

wes
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A very important part that is spelled at 1:16, but was not mentioned anywhere else in the video, is that a>b. Without mentioning it, the solution gives an impression, as if the answer is always a, despite the expression being symmetric with regards to its arguments (that is, if you switch a and b places inside of it, the expression would still be the same). In fact, the case when b>a would evaluate to exactly b (the solution looks exactly as the one presented in the video, but starting out by factoring out b instead of a).

supermario
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can i ask where you found this problem?

pokepros
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