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3 votes

It is in  1∞ form,so we can write,

limx->∞   [(x2+5x+3)/(x2+x+2)] = limx->∞  ex[(x^2 +5x+3)/(x^2+x+2) -1]  = limx->∞  ex[(4x+1)/(x^2+x+2)]  limx->∞  e(4x^2 +1)/(x^2+x+2)  = e (since x-> ∞, taking only highest power in both numerator and denominator. 

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