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What a difference two roots make ! (Posted on 2008-05-24) Difficulty: 2 of 5
Evaluate:

Limit ( (√(y + √(y + √y))) - √y)
y → ∞

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Not quite Calculus | Comment 2 of 5 |
Allowing "y" to be 1, the square root of y is 1.
Under the innermost radical the value is 2.
Stepping through to the next radical we carry through
the sq. root of 2 and so have a value of 2.4142...

The value of the radical nest comes out at 1.55377..
With the subtraction of single y radical we achieve a
value of 0.55377.....

As we increase the value of y the nested group increases
but so does the single y radical.  While its value closes
upon the nested group, the expression will only equal 0.5
in the defined limit.
  Posted by brianjn on 2008-05-24 22:00:33
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