4 votes 4 votes $\lim_{x \rightarrow \infty} \left(\frac{x^{2} + 5x +3}{x^{2} + x + 2}\right)^{x}$ Calculus limits calculus + – bahirNaik asked Dec 30, 2015 edited Jan 27, 2016 by makhdoom ghaya bahirNaik 442 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 6 votes 6 votes Ans is e^4 resuscitate answered Dec 30, 2015 selected Dec 30, 2015 by Pooja Palod resuscitate comment Share Follow See 1 comment See all 1 1 comment reply bahirNaik commented Dec 30, 2015 reply Follow Share thanks @Sayantan Ganguly :) 0 votes 0 votes Please log in or register to add a comment.
3 votes 3 votes It is in 1∞ form,so we can write, limx->∞ [(x2+5x+3)/(x2+x+2)]x = 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) = e4 (since x-> ∞, taking only highest power in both numerator and denominator. Shashank Kumar answered Dec 31, 2015 Shashank Kumar comment Share Follow See all 0 reply Please log in or register to add a comment.