Question

等价无穷小求解，过程详细？

Answer 1

左边
=ln[(1-ax^2)/(1+ax^2)]
=ln{(1-ax^2)[1-ax^2+o(x3)]}
~ln[1-2ax^2+o(x3)]
~-2ax^2+o(x3)
右边
~{sin[(根号6)*x]}^2
~6[x+o(x^2)]^2
~6x^2+o(x^3)
-2a=6，
a=-3

Answer 2

根据题意，lim(x->0) ln[(1-ax^2)/(1+ax^2)]/[(x^4)/10000+sin^2(√6x)]=1
lim(x->0) [ln(1-ax^2)-ln(1+ax^2)]/[(x^4)/10000+sin^2(√6x)]=1
lim(x->0) [(-2ax)/(1-ax^2)-(2ax)/(1+ax^2)]/[(x^3)/2500+√6*sin(2√6x)]=1
lim(x->0) (-4ax)/[(1-a^2*x^4)*(x^3)/2500+(1-a^2*x^4)*√6*sin(2√6x)]=1
lim(x->0) (-4a)/[(3x^2)/2500-(7a^2*x^6)/2500+12cos(2√6x)*(1-a^2*x^4-4a^2*x^3)]=1
-4a/12=1
a=-3

Answer 3