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What is the derivative of [ tanx] where [•] indicates greatest integer function?

What is the derivative of [ tanx] where [•] indicates greatest integer function?

Grade:12

1 Answers

Nandana
110 Points
4 years ago
hi,
  It’s really fantastic question ! I’m so glad to answer this question
     firstly , let us see what is greatest integer function ?
         in Mathematics it is named as ‘Floor’ function ,
          Floor (x) is the largest integer less than or equal to ‘x’
              Ex: Floor(4.5) = 4
         & one more thing Floor function follows the identity that
           Floor (x+n) = n+ Floor(x) , where ‘n ‘ is an integer 
       now, coming to the question ,
            d/dx(Floor(tanx)) = sec2(x) Floor(tan x),
         but in walfram they give it as Floor’(tan x) but they didn’t show the plot
                so , I’m also confused but I think they plot Dirac Delta functions infinitely by integrating them again we get same Floor function I think !
 
 
 
        
               
 
         
                       
              

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