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lim x tends to infinity [(x^2+5x+3)/(x^2+x+2)]^x=?

lim x tends to infinity [(x^2+5x+3)/(x^2+x+2)]^x=?

Grade:12th pass

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
lim x tends to infinity [(x^2+5x+3)/(x^2+x+2)]^x
=e^lim x tends to infinity x.[(x^2+5x+3)/(x^2+x+2)-1]
=e^lim x tends to infinity x.(4x+1)/(x^2+x+2)
=e^lim x tends to infinity 4x^2(1+1/x)/x^2(1+1/x+2/x^2)
=e^lim x tends to infinity4(1+1/x)/(1+1/x+2/x^2)
applying limit, we get
e^4 Ans.
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty


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