请问lim(x→1) (3x+5)/(x^3-1) 怎样求?
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请问lim(x→1) (3x+5)/(x^3-1) 怎样求?
![请问lim(x→1) (3x+5)/(x^3-1) 怎样求?](/uploads/image/z/19502165-29-5.jpg?t=%E8%AF%B7%E9%97%AElim%28x%E2%86%921%29+%283x%2B5%29%2F%28x%5E3-1%29+%E6%80%8E%E6%A0%B7%E6%B1%82%3F)
(3x+5)/(x^3-1)=(3X+5)/(X-1)(X^2+X+1)
=3(X-1)/(X-1)(X^2+X+1)+8/(X^3-1)
=3/[(X^2+X+1/4)+2/4]+8/(X^3-1)
=3/[(X+1/2)^2+3/4] + 8/(X^3-1)
令X=1,则原式=1+∞=∞
=3(X-1)/(X-1)(X^2+X+1)+8/(X^3-1)
=3/[(X^2+X+1/4)+2/4]+8/(X^3-1)
=3/[(X+1/2)^2+3/4] + 8/(X^3-1)
令X=1,则原式=1+∞=∞
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