You have forgot to mention when x tends to " zero " If its right then the solution is as follows ----
Lt x→₀ [ (1 - ³√x ) / ( x - 1 ) ] = ?
Put [ ³√x ] = y so that as Lt x→₀ y also tends to zero .
=> Lt x→₀ [ (1 - ³√x ) / ( x - 1 ) ] = Lt y→₀ [ (1 - y ) / ( y³ - 1 ) ]
=> Lt y→₀ (1 - y ) / [ ( y - 1 ) ( y^2 + 2 y + 1 ) ]
=> ( - ) Lt y→₀ [ 1 / ( y^2 + 2 y + 1 ) ]
=> - 1 ………………………. Answer Answer
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You have forgot to mention when x tends to " zero " If its right then the solution is as follows ----
Lt x→₀ [ (1 - ³√x ) / ( x - 1 ) ] = ?
Put [ ³√x ] = y so that as Lt x→₀ y also tends to zero .
=> Lt x→₀ [ (1 - ³√x ) / ( x - 1 ) ] = Lt y→₀ [ (1 - y ) / ( y³ - 1 ) ]
=> Lt y→₀ (1 - y ) / [ ( y - 1 ) ( y^2 + 2 y + 1 ) ]
=> ( - ) Lt y→₀ [ 1 / ( y^2 + 2 y + 1 ) ]
=> - 1 ………………………. Answer Answer
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
.