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anonymous
 5 years ago
CALCULUS QUESTION:
Using l'Hopital's Rule evaluate the following limit:
lim (1 + 5/x)^(x/4) as x >+infinity
anonymous
 5 years ago
CALCULUS QUESTION: Using l'Hopital's Rule evaluate the following limit: lim (1 + 5/x)^(x/4) as x >+infinity

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you substitute in infinity for x you first get 1^(infinity) which is indeterminate. So you have to manipulate the equation. If you set the limit equal to L and take the ln of both sides you end up with ln(L) = lim x> infinity [(1+5/x)]^(x/4) which is equivalent to ln(L) = lim x> infinity (x/4)[(1+5/x)]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is now at the stage of an infinity times 0. So put the x in the denominator to get ln(L) = lim x> infinity (1/4)ln[(1+5/x)]/x^(1) to force a 0/0 case and take the derivatives of the numerator and denominator to get a messy equation to simplifies to ln(L) = lim x> infinity 5/[4(1 + 5/x)] or just ln(L) = 5/4 so L = e^(5/4)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you remember that lim x>infinity (1 + 1/x)^(x) = e then the solution should make sense even if the explanation is confusing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah that makes sense, thank you
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