证明n趋向无穷时,5n^2/(7n-n^2)的极限等于-5

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证明n趋向无穷时,5n^2/(7n-n^2)的极限等于-5证明n趋向无穷时,5n^2/(7n-n^2)的极限等于-5证明n趋向无穷时,5n^2/(7n-n^2)的极限等于-5lim5n^2/(7n-n

证明n趋向无穷时,5n^2/(7n-n^2)的极限等于-5
证明n趋向无穷时,5n^2/(7n-n^2)的极限等于-5

证明n趋向无穷时,5n^2/(7n-n^2)的极限等于-5
lim5n^2/(7n-n^2)
上下同除n^2
=lim(5/(7/n-1))
=5/(lim7/n-1)
=5/(0-1)
=-5

原式=lim(n->∞) 5/(7/n-1)
=5/(0-1)
=-5

lim5n^2/(7n-n^2)
上下同除n^2
那么
原式=lim(5/(7/n-1))
=5/(lim7/n-1)
=5/(0-1)
=-5