perplexus.info :: Calculus : Rooting For The Limit

Rooting For The Limit (Posted on 2008-04-23)

Evaluate:

Limit ((2^y + 2^2y + 2^3y)/3)^1/y
y → 0

Bonus Question:

Work out the following limit:

Limit ((2^y + 6^y + 18^y)/3)^1/y
y → 0

See The Solution Submitted by K Sengupta

Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

computer exploration (possible spoiler)

| Comment 1 of 6

Programs like

10   Y=1
20   for I=1 to 150
30    V=((2^Y+4^Y+8^Y)/3)^(1/Y)
40    print "    ";Y,1/Y,V
50    Y=Y/2
60   next

and

10   Y=1
20   for I=1 to 150
30    V=((2^Y+6^Y+18^Y)/3)^(1/Y)
40    print "    ";Y,1/Y,V
50    Y=Y/2
60   next

using the extended precision of UBASIC,

make it seem the respective answers are 4 and 6.

Posted by Charlie on 2008-04-23 11:36:44

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