Question

求数学大神

求解





Answer 1

（1）分子分母同求导
=lim（secx)^2/5(sec5x)^2 = (cos5x)^2 /5(cosx)^2
继续求导
=lim10cos5xsin5x/10cosxsinx = sin10x/sin2x
继续

=lim10cos10x/2cos2x
代入
=10/2=5
（2）求导
=lim 8/（1+8x）/1=8/（1+8x）=8
（3）x^3-8=（x-2)(x^2+2x+4)
所以lim1/（x-2）-12/(x^3-8)
=lim(x^2+2x+4-12)/[（x-2)(x^2+2x+4)]
=lim(x^2+2x-8)/[（x-2)(x^2+2x+4)]
=lim(x-2)(x+4))/[（x-2)(x^2+2x+4)]
=lim(x+4)/(x^2+2x+4)
将x=2代入 得1/2

Answer 2

看不太清楚，你写个清楚的呗

追问

Answer 3

(4)
lim(x->2) [ 1/(x-2) -12/(x^3-8) ]
=lim(x->2) [(x^2+2x+4) -12]/[(x-2)(x^2+2x+4)]
=lim(x->2) (x^2+2x-8)/[(x-2)(x^2+2x+4)]
=lim(x->2) (x-2)(x+4)/[(x-2)(x^2+2x+4)]
=lim(x->2) (x+4)/(x^2+2x+4)
=(2+4)/(4+4+4)
=6/12
=1/2
(5)
lim(x->0) ln(1+8x)/x
=lim(x->0) 8x/x
=8
(6)
let
y= π/2-x
lim(x->π/2) tanx/tan(5x)
=lim(y->0) cotx/cot(5x)
=lim(y->0) tan(5x)/tanx
=lim(y->0) 5x/x
=5

Answer 4

我认为还是作业帮可靠