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Science Forum Forum Index » Mathematics » Find the LHD. - Quick answer pls

  
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Ironmaiden
Posted: Fri Jul 04, 2008 11:46 pm    Post subject: Find the LHD. - Quick answer pls Reply with quote

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QUICK ANSWER PLEASE

What is the left hand derivative of:

f(x) = [x] sin(pi x) at x = k where [x] denotes the greatest integer function and k is an integer.

Please give the answer in detail.
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serpicojr
Posted: Sat Jul 05, 2008 4:04 pm    Post subject: Reply with quote

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Well, in the interval [k-1,k), the function is given by:

f(x) = (k-1)sin(π x)

And f(k) = 0 = (k-1)sin(π k). So the left hand derivative of f(x) at k is the same as the usual derivative of (k-1)sin(π x) at k.
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