Question

求高数大佬帮忙做做

Answer 1

追问

你这是有答案吗

追答

没有答案，都是我自己写的。

Answer 2

(1)
x->0
e^(bx) = 1+bx+ o(x)
ax+e^(bx) = 1+(a+b)x +o(x)
lim(x->0) [ ax+e^(bx) ]^(1/x)
=lim(x->0) [ 1+(a+b)x ]^(1/x)
=e^(a+b)
(2)
xy+e^y-e =0

x=0
0+e^(y(0)) - e =0
y(0) =1
xy+e^y-e =0
y + xy' + e^y .y' = 0
(x+e^y) y' = -y
y' = -y/(x+e^y)
y'(0) = -y(0) /[ 0 + e^(y(0)) ] = -1/( 0+ e) =-1/e
y' = -y/(x+e^y)
y'' =-[ (x+e^y)y' - y(1 + e^y .y') ] /(x+e^y)^2
y''(0) = -[ (0+e)(-1/e) - (1 + e .(-1/e) ) ] /(0+e)^2
= -[ -1 - ( 1-1) ]/ e^2
=1/e^2
(3)
f(x) =∫(0->x) cos(x-t)^2 dt
f'(x) = cos(x-x)^2 = cos0 =1