Question

lim(x→1)(x³＋2x＋a)/(x－1)＝b，求a＝？，b＝？求过程，那个不能直接用洛

Answer 1

lim(x→∞)[(2x²+1)/(x-1)
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ax
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b]
=lim(x→∞)[(2-a)x^2+(a-b)x+1+b]/(x-1)]
若2-a不等于0，则这个极限是无穷大
所以2-a=0
a=2
所以lim(x→∞)[(2x²+1)/(x-1)
-
ax
-
b]
=lim(x→∞)[(2-a)x^2+(a-b)x+1+b]/(x-1)]
=lim(x→∞)[(2-b)x+1+b]/(x-1)]
=lim(x→∞)[(2-b)+(1+b)/x]/(1-1/x)]
=(2-b)/1
=2-b=0
b=2