Question

高数题怎么做

Answer 1

写的比较乱，希望你能看懂

Answer 2

dy/dx +y = e^(-x)
let
y= (Ax+B)e^(-x)
y' =[-(Ax+B) +A].e^(-x) = [-Ax+(A-B)].e^(-x)
y'+y=e^(-x)
[-Ax+(A-B)].e^(-x) + (Ax+B)e^(-x) =e^(-x)
Ae^(-x) = e^(-x)
A=1
通解
y= (x+B)e^(-x)

Answer 3

x->0
分母
e^(x^2) -1 = x^2 +o(x^2)
分子
ln(1-x) = -x -(1/2)x^2 +o(x^2)
sinx . f(x)
=[ x+o(x) ] . [ f(0) + f'(0)x +o(x) ]
=[ x+o(x) ] . [ 1 + f'(0)x +o(x) ]
= x + f'(0)x^2 +o(x^2)
ln(1-x) +sinx . f(x)
=[-x -(1/2)x^2 +o(x^2)] +[x + f'(0)x^2 +o(x^2)]
= [-1/2 +f'(0) ]x^2 +o(x^2)
lim(x->0 ln(1-x) + sinx.f(x) /[e^(x^2) -1] =0

=>
-1/2 +f'(0) = 0
f'(0) = 1/2