perplexus.info :: Calculus : Getting Powerful With Euler

Getting Powerful With Euler (Posted on 2009-07-28)

Evaluate:

            (1 + y)^1/y - e
Limit   ----------------
y → 0          y

Note: e denotes the Euler’s number.

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.)

numeric answer

| Comment 1 of 3

UBASIC:

10   point 27
15   Y=0.5
20   for I=1 to 90
30     Y=Y/2
40     V=((1+Y)^(1/Y)-exp(1))/Y
50     print V
60   next

finds as the last two entries:

-1.35914091422952261768014373466991806904782567601876021709242718939902979642034
43495191498776452040027027579776751902846568026719688
-1.35914091422952261768014373517312465896322461143437000209395032049981367026803
53262908086216604099891709330087862649963007995599441

so an approximation is:

-1.359140914229522617680143735

Posted by Charlie on 2009-07-28 12:31:41

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