Question

lim x->∞ 3n^2 +4n-1/3n^2 +2n +7)^2n +5

Answer 1

$lim_{n to infty} left(cfrac{3n^2+4n-1}{3n^2+2n+7}right)^{2n+5}= lim_{n to infty} left(1+cfrac{2n-8}{3n^2+2n+7}right)^{2n+5}=\= lim_{n to infty} left(1+cfrac{1}{cfrac{2n-8}{3n^2+2n+7}}right)^{tfrac{3n^2+2n+7}{2n-8}cdot(2n+5)cdottfrac{2n-8}{3n^2+2n+7}}=\= lim_{n to infty} e^{(2n+5)cdottfrac{2n-8}{3n^2+2n+7}}=e^{tfrac{4}{3}}=sqrt[3]{e^4}$