Evaluate the following:
(i) Limit floor(abs(n))/abs(floor(n))
(ii) ∫abs(floor(x)) dx
This seems a bit easy but here's that I got.
evaluates to 1 for all integers and for all positive real numbers. For negative non-integers where abs(n) is between consecutive whole numbers a and a+1 the function evaluates to a/(a+1) which also goes to 1.
The negative part is just the sum of the numbers 1 to 2012 and the positive part is just the sum of the numbers 0 to 502.
2012*2013/2 + 502*503/2 = 2151331
The integral of the first function would have been a bit harder...
Posted by Jer
on 2012-08-17 14:08:37