求这两道题的极限,我会给您的诚意加分的!lim┬(x→1)⁡(3/(1-x^3)-2/(1-x))；lim┬(x→∞)⁡{x[ln⁡(x+3)-ln⁡x]}

Question

求这两道题的极限 ,我会给您的诚意加分的!
lim┬(x→1)⁡(3/(1- x^3 )- 2/(1-x)) ；lim┬(x→∞)⁡{x[ln⁡(x+3)- ln⁡x ] }

Answer 1

lim┬(x→1)⁡(3/(1- x^3 )- 2/(1-x))
=lim┬(x→1)⁡(1-2x-2x^2)/(1-x^3)
∵当x→1时,1-x^3→0,1-2x-2x^2→-3≠0
∴lim┬(x→1)⁡((1-x^3)/(1-2x-2x^2)=0
∴lim┬(x→1)⁡(3/(1- x^3 )- 2/(1-x))
=lim┬(x→1)⁡(1-2x-2x^2)/(1-x^3)
=-∞
lim┬(x→∞)⁡{x[ln⁡(x+3)- ln⁡x ] }
=lim┬(x→1)⁡{x*ln[(x+3)/x]}
=lim┬(x→1)⁡[x*ln(1+3/x）]
≤lim┬(x→1)⁡（x*ln1）
=lim┬(x→1)⁡ln1^x
=lim┬(x→1)⁡ln1
=0