Question

如图，高数第一章，请问怎么求的a和b？

Answer 1

因为等价，所以商的极限为1，利用等价无穷小代换和洛必达可以求出结果。

Answer 2

x->0
f(x)=∫0->x^2) ln(1+t) dt ~ g(x) = x^a.( e^(bx) -1 )
To find : a,b
solution
t->0
ln(1+t) = t +o(t)
f(x)
=∫0->x^2) ln(1+t) dt
=∫0->x^2) ( t+o(t) ) dt
=(1/2)x^4 +o(x^4)
x->0
e^(bx)-1 = bx +o(x)
x^a.( e^(bx) -1 ) = bx^(a+1) +o(x^(a+1))
f(x)=∫0->x^2) ln(1+t) dt ~ g(x) = x^a.( e^(bx) -1 )
(1/2)x^4 +o(x^4) =bx^(a+1) +o(x^(a+1))
b=1/2 and a=3