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Sandeep Kumar Maurya

_{[x^x ]}

_{[1/2 ]} (sin3[x])/[x] where [.] is GIF

as [ ] is for greatest integer function [1/2] = [0.5] = 0

and _{[x^x ]}

0

therefore for any value of x this limit is tends to 0.

hence,

_{[x^x ]}

_{[1/2 ]} (sin3[x])/[x] = _{[x^x ]}

₀ (sin3[x])/[x]

= _{[x^x ]}

₀ { (sin 3[x] ) / 3[x] } * 3

thus _{[x^x ]}

₀ { (sin 3[x] ) / 3[x] } = 1

= 1 * 3 = 3

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