Lim(x->∞)[ln(1+3*x^2)]/[ln(3+x^4)]
=Lim(x->∞)[ln(1+3*x^2)]‘/[ln(3+x^4)]’
=Lim(x->∞)[6x/(1+3*x^2)]/[4x³/(3+x^4)]
=Lim(x->∞)[6x(3+x^4)]/(1+3*x^2)4x³]
=Lim(x->∞)[6(3/x^4+1)]/4(1/x^2+3)]
=6/12=1/2
Lim(x->∞)[ln(1+3*x^2)]/[ln(3+x^4)]
=Lim(x->∞)[ln(1+3*x^2)]‘/[ln(3+x^4)]’
=Lim(x->∞)[6x/(1+3*x^2)]/[4x³/(3+x^4)]
=Lim(x->∞)[6x(3+x^4)]/(1+3*x^2)4x³]
=Lim(x->∞)[6(3/x^4+1)]/4(1/x^2+3)]
=6/12=1/2