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Differential Calculus

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19 Jan 2012 01:08:42 IST

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find the range

Mathematics

if f(x)=[x^2]-[x}^2 , where [.] denotes the greatest integer function and x belongs to [0,n];n belongs to natural no.,then the number of elements in the range of f(x) is

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Arjun Virmani

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19 Jan 2012 14:25:27 IST

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the range of [x^2] = n^2 but since we are gonna subtract the same thrfr we'll go for a smaller unit.

x just less than n

[x^2] = n^2 - 1

[ x ] = n-1

[ x ]^2 = (n-1)^2...............

Range = integars between [0 , n^2 - 1 - (n-1)^2]................!!!

jagdish singh

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20 Jan 2012 18:39:17 IST

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$\hspace{-16}$I am also Getting No. of Element in Range of $\mathbf{f(x)=\lfloor x^2 \rfloor-\lfloor x \rfloor}$\\\\ is $\mathbf{=2n}$\\\\ Like $\mathbf{\mathbb{R_{f(x)}}=\left\{0,1,2,3,........,2n-1\right\}}$$

jagdish singh

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20 Jan 2012 18:40:43 IST

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$\hspace{-16}$I am also Getting No. of Element in Range of $\mathbf{f(x)=\lfloor x^2 \rfloor-\lfloor x \rfloor^2}$\\\\ is $\mathbf{=2n}$\\\\ Like $\mathbf{\mathbb{R_{f(x)}}=\left\{0,1,2,3,........,2n-1\right\}}$$

shivansh shrivastava

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20 Jan 2012 19:51:37 IST

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Range:{0,2n-1}

Akshay

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20 Jan 2012 20:14:50 IST

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Range:{0,1,2,....,2n-2}

Abhishek Bandiya

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20 Jan 2012 22:28:44 IST

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find the range

Abhishek Bandiya

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20 Jan 2012 22:29:52 IST

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ARJUN AND AKSHAY ARE CORRECT

RANGE IS {0,1,2...............2n-2}

jagdish singh

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22 Jan 2012 15:37:12 IST

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Yes Abhishek you are saying Right.actually there was a typing Mistake.Thanks

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