lim x(x+2)/x^2 (x→oo)lim 1/sin(x-2) (x→2)

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lim x(x+2)/x^2 (x→oo)lim 1/sin(x-2) (x→2)

lim x(x+2)/x^2 (x→oo)lim 1/sin(x-2) (x→2)
lim x(x+2)/x^2 (x→oo)
lim 1/sin(x-2) (x→2)

lim x(x+2)/x^2 (x→oo)lim 1/sin(x-2) (x→2)
lim x(x+2)/x^2
=lim (x+2)/x
=lim(1+2/x)=1
2 sin(x-2)趋于0
lim1/sin(x-2)=无穷,极限不存在

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lim x(x+2)/x^2=lim(x+2)/x=1 (x→oo) 极限为1
lim 1/sin(x-2) x→2,sin(x-2)→0,所以lim 1/sin(x-2)→oo,没有极限