Question

求图中的极限

Answer 1

(1)
lim(x->1) [ 1/(1-x) - 3/(1-x^3)]
=lim(x->1) [ (1+x+x^2) -3 ]/[(1-x)(1+x+x^2)]
=lim(x->1) (x^2+x-2)/[(1-x)(1+x+x^2)]
=lim(x->1) (x-1)(x+2)/[(1-x)(1+x+x^2)]
=lim(x->1) -(x+2)/(1+x+x^2)
=-1
(3)
lim(x->4) [√(2x+1) -3 ]/[√(x-2) -√2]
=lim(x->4) [√(2x+1) -3 ].[√(x-2) +√2] /(x-4)
=2√2.lim(x->4) [√(2x+1) -3 ] /(x-4)
=2√2.lim(x->4) [(2x+1) -9 ] /{ (x-4).[√(2x+1) +3 ] }
=4√2.lim(x->4) { 1/[√(2x+1) +3 ] }
=(4√2)(1/6)
=2√2/3
(5)
lim(x->0) (tanx -sinx)/x^2 (0/0)
=lim(x->0) [(secx)^2 -cosx]/ (2x) (0/0)
=lim(x->0) [2(secx)^2.tanx -sinx]/2
=0

追问

第七道会吗😂

追答

(7)
lim(x->1) sin(x-1)/(x^2-1)
=lim(x->1) sin(x-1)/[(x-1)(x+1)]
=lim(x->1) 1/(x+1)
=1/2

追问

感谢大神~