Question

求极限：limx趋向于0 (e)^(x)^2-1/ln(1+3x^2)

Answer 1

limx趋向于0 [e^(x^2)-1]/ln(1+3x^2)]

用洛必达法则：

[e^(x^2)-1/ln(1+3x^2)]'=2xe^(x^2)

[ln(1+3x^2)]'=6x/(1+3x^2)

[2xe^(x^2)]/[6x/(1+3x^2)=(1/3+x^2)e^(x^2)

limx趋向于0 [e^(x^2)-1]/ln(1+3x^2)]=limx趋向于0 (1/3+x^2)e^(x^2)=1/3.