In article <9501280255.AA27284@rigel.cc.umanitoba.ca>, Barry Wolk
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.
Dept of Mathematics
University of Manitoba
Winnipeg Manitoba Canada
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