Lim х стремится к бесконечности ((x^2+x+1)/(x^2+4x-1))^(-3x^2)

Question

Lim х стремится к бесконечности ((x^2+x+1)/(x^2+4x-1))^(-3x^2)

Answer 1

=lim ((x^2 +4x-1 -3x+2)/(x^2+4x-1))^(-3x^2) 
=lim (1 + (2-3x)/(x^2+4x-1))^(-3x^2) =
=lim [(1 + (2-3x)/(x^2+4x-1))^ ((x^2+4x-1)/(2-3x))] ^((2-3x)/(x^2+4x-1)) (-3x^2)
=exp(lim(2-3x)(-3x^2)/(x^2+4x-1)) ) = exp lim (9x^3+...)/(x^2+4x-1) =
exp(+inf) = +inf