Question

高数题能找人帮解答吗？

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Answer 1

4.6
(1)
lim(x->0) ln(1-2x)/x^2
=lim(x->0) (-2x)/x^2
不存在
(2)
lim(x->无穷) lnx/x^n
洛必达
=lim(x->无穷) (1/x)/[nx^(n-1)]
=lim(x->无穷) 1/[nx^n]
=0
(3)
lim(x->无穷) x^n/e^x
洛必达n次
=lim(x->无穷) n!/e^x
=0
(4)
lim(x->0+) x^x
=lim(x->0+) e^(lnx/x)
洛必达
=lim(x->0+) e^(1/x)
=e^0
=1
(1)
y=x^3-6x^2+9x-30
y'=3x^2-12x+9
y'=0
3x^2-12x+9=0
x^2-4x+3=0
(x-1)(x-3)=0
x=1 or 3 (rej)
y''=6x-12
y''(1)=6-12=-6<0 (max)
max y =y(1)=1-6+9-30 =-26
y(-2)=-8-24-18-30=-80
y(2)=8-24+18-30=-28
min y = y(-2)=-80
(2)
y
=-x^2+6x-4
=-(x^2-6x +9) +5
=-(x-3)^2 +5
max y =5