Question

(2)(4)求极限怎么做？

求大神指点

Answer 1

(2)
lim(x->∞) (x-1)(x-2)(x-3)/(1-4x^3)
分子分母同时除以 x^3
=lim(x->∞) (1-1/x)(1-2/x)(1-3/x)/(1/x^3 -4)
=(1-0)(1-0)(1-0)/(0-4)
=-1/4
(4)

lim(x->1) [√(3-x) -√(1+x)]/(x^2-1)
=lim(x->1) [(3-x) -(1+x)]/ { (x^2-1).[√(3-x) +√(1+x)] }
=lim(x->1) 2(1-x)/ { (x^2-1).[√(3-x) +√(1+x)] }
=lim(x->1) -2/ { (x+1).[√(3-x) +√(1+x)] }
=-2/[ (1+1) . ( √2 +√2) ]
=-1/(2√2)
=-√2/4

Answer 2

解如下图所示