作业帮求极限lim((1-x)^0.5-3)/(2+x^(1/3)) (x趋近于-8)
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求极限lim((1-x)^0.5-3)/(2+x^(1/3)) (x趋近于-8)
分子分母同乘：[√(1-x) + 3 ] [(4+2*x^(1/3)+x^(2/3))] 有理化：
lim(x->-8) [√(1-x) -3 ] /(2+x^(1/3))
=lim(x->-8) [(1-x) - 9 ][(4+2*x^(1/3)+x^(2/3))] / {(8+x)*[√(1-x) + 3 ]}
=lim(x->-8) -[(4+2*x^(1/3)+x^(2/3))] / [√(1-x) + 3 ]
= -[4-4+4]/[3+3]
= -2/3
lim(x->-8) [√(1-x) -3 ] /(2+x^(1/3))
=lim(x->-8) [(1-x) - 9 ][(4+2*x^(1/3)+x^(2/3))] / {(8+x)*[√(1-x) + 3 ]}
=lim(x->-8) -[(4+2*x^(1/3)+x^(2/3))] / [√(1-x) + 3 ]
= -[4-4+4]/[3+3]
= -2/3
求极限lim((1-x)^0.5-3)/(2+x^(1/3)) (x趋近于-8)
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