In article <9501280255.AA27284@rigel.cc.umanitoba.ca>, Barry Wolk
<wolk@ccm.umanitoba.ca> wrote:
Here is my favorite "paradox", more accurately described as "find the error".
It involves calculus, but so did some recent posts in this thread.

Define the function
f(x) = 2 arcsin(x) + arcsin( 1  2 x^2 ).
So f(x) is defined for x in the interval [1, 1].

Differentiate and simplify: find f'(x) = ??

Check the unexpected answer for f'(x) by calculating f(0) and f(1).
No problem so far  these values do not contradict a fundamental
theorem of calculus.

Recheck f'(x) by calculating f(1). *NOW* we have a problem.

Find your error. Don't tell me that you didn't make a mistake
in Step 2  everybody does.
Cute, eh?
Barry Wolk
Dept of Mathematics
University of Manitoba
Winnipeg Manitoba Canada
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