这个11题怎么做啊!!
1个回答
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11.
lim [3/(1-x³)- 1/(1-x)]
x→1
=lim [1/(x-1) -3/(x³-1)]
x→1
=lim [(x²+x+1)/(x-1)(x²+x+1) -3/(x-1)(x²+x+1)]
x→1
=lim (x²+x+1-3)/[(x-1)(x²+x+1)]
x→1
=lim (x²+x-2)/[(x-1)(x²+x+1)]
x→1
=lim (x-1)(x+2)/[(x-1)(x²+x+1)]
x→1
=lim (x+2)/(x²+x+1)
x→1
=(1+2)/(1²+1+1)
=3/3
=1
lim [3/(1-x³)- 1/(1-x)]
x→1
=lim [1/(x-1) -3/(x³-1)]
x→1
=lim [(x²+x+1)/(x-1)(x²+x+1) -3/(x-1)(x²+x+1)]
x→1
=lim (x²+x+1-3)/[(x-1)(x²+x+1)]
x→1
=lim (x²+x-2)/[(x-1)(x²+x+1)]
x→1
=lim (x-1)(x+2)/[(x-1)(x²+x+1)]
x→1
=lim (x+2)/(x²+x+1)
x→1
=(1+2)/(1²+1+1)
=3/3
=1
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