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Rooting For The Limit (Posted on 2008-04-23) Difficulty: 2 of 5
Evaluate:

Limit ((2y + 22y + 23y)/3)1/y
y → 0


Bonus Question:

Work out the following limit:

Limit ((2y + 6y + 18y)/3)1/y
y → 0


See The Solution Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 3 of 6 |
(In reply to Solution by hoodat)

But if 1/y approaches infinity "faster" than the value in parentheses approaches 1, then the number raised to the power could be other than 1.

For example, as y approaches zero, (1+y)^(1/y) approaches, not 1, but rather e, the basis of "continuous compounding" for example.

In the current example of the first part of this problem, when y = 1/713623846352979940529142984724747568191373312, the portion inside parentheses is about 1.00000000000000000000000000000000000000000000194261215933945611783779011590634 and being raised to the 1/y power brings about          4.000000000000000000000000000000000000000000000897677427445074158301347400319084843059343712861


  Posted by Charlie on 2008-04-23 17:23:23
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