(x^4+2x^2-3)/(x^2-3x+2)当x→1时是无穷小量还是无穷大量

Question

(x^4+2x^2-3)/(x^2-3x+2) 当x→1时是无穷小量还是无穷大量

Answer 1

(x^4+2x^2-3)/(x^2-3x+2) =(x²+3)(x²-1)/(x-2)(x-1)
=(x²+3)(x-1)(x+1)/(x-2)(x-1)
=(x²+3)(x+1)/(x-2)
当x→1时,
lim(x²+3)(x+1)/(x-2)=-8
所以他的极限为实数-8,不是无穷大或者无穷小