Question

f (x)=x×sinax与g(x)=x²ln(1-bx)

高数!当x趋于0时,f(x)=x-sinax与g(x)=(x^2)ln(1-bx)为等价
当x趋于0时,f(x)=x-sinax与g(x)=(x^2)ln(1-bx)为等价无穷小,则a=?,b=?

Answer 1

g(x)~-bx^3
limf(x)/g(x)=-lim(x-sinax)/bx^3=-lim(1-acosax)/3bx^2=-lim(1- cos x)/3bx^2=-lim( x^2 /2)/3bx^2=-1/6b=1
b=-6
lim(1-acosax)=0,a=1