Question

求下列函数的极限

求下列函数的极限求下列函数的极限

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Answer 1

(1)lim(x->0) (4x^3-2x^2+4x)/(x^2+2x) =lim(x->0) (4x^2-2x+4)/(x+2) = 4/2 = 2
(2)lim(x->1) (x^3-4x+6)/(3x^2+1) = (1-4+6)/(3+1) = 3/4
(3)
lim(x->0) x/[√(1+x) -1 ]
=lim(x->0) x.[√(1+x) +1 ]/x
=lim(x->0) [√(1+x) +1 ]
=2
(4)
lim(x->∞) (x^2-2x+3)/(3x^2+4)
= lim(x->∞) (1-2/x+3/x^2)/(3+4/x^2)
=1/3
(5)
lim(x->∞) (x^2-3x+1)/(x^3+2x^2+8)
=lim(x->∞) (1-3/x+1/x^2)/(x+2+8/x^2)
=0
(6)
lim(x->2) (x-2)/(2+x)
=0
(7)
lim(x->∞) (x+6)/(3x^2+x+3)
=lim(x->∞) (1+6/x)/(3x+1+3/x)
=0
(8)
lim(x->1) (x^2-1)/(x^2-3x+2)
=lim(x->1) (x-1)(x+1)/[(x-1)(x-2)]
=lim(x->1) (x+1)/(x-2)
=-2