Simple limit as x approaches infinity problem?

.. lim (x→∞) { x / [ 2x + √(4x²+x) ] } ......... Divide Num. & Den. both by x

= lim (x→∞) 1 / { [ 2x + √(4x²+x) ] / x } ... Now write Den. x as √(x²)

= lim (x→∞) 1 / { [ (2x)/(x) ] + [ √(4x²+x) / √(x²) ] }

= lim (x→∞) 1 / { 2 + √[ 4 + ( 1/x ) ] }

= 1 / { 2 + √( 4 + 0 ) }

= 1 / { 2 + 2 }

= 1 / 4 ................................. Ans.

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