设lim(x→-1)(x^3-ax눀-x+4)⼀(x+1)有极限l,求a,l的值

2024-11-16 17:35:23
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回答(1):

x->-1有极限,那么(x^3-ax^2-x+4)/(x+1)一定是0/0型,即-1-a+1+4=0,a=4
x^3-4x^2-x+4=x^3+x^2-5x^2-5x+4x+4=(x+1)(x^2-5x+4)=(x+1)(x-1)(x-4)
∴lim(x→-1)(x^3-ax²-x+4)/(x+1)
=lim(x→-1)(x+1)(x-1)(x-4)/(x+1)
=lim(x→-1)(x-1)(x-4)
=-2*(-5)
=10