已知lim[(3n^2+cn+1)/(an^2+bn)-4n]=5,求常数a、b、c的值
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已知lim[(3n^2+cn+1)/(an^2+bn)-4n]=5,求常数a、b、c的值
![已知lim[(3n^2+cn+1)/(an^2+bn)-4n]=5,求常数a、b、c的值](/uploads/image/z/8532463-31-3.jpg?t=%E5%B7%B2%E7%9F%A5lim%5B%283n%5E2%2Bcn%2B1%29%2F%28an%5E2%2Bbn%29-4n%5D%3D5%2C%E6%B1%82%E5%B8%B8%E6%95%B0a%E3%80%81b%E3%80%81c%E7%9A%84%E5%80%BC)
lim[(3n^2+cn+1)/(an^2+bn)-4n]=lim[(3n^2+cn+1-4an^3-4bn^2)/(an^2+bn)]
则-4a=0 即a=0
极限化成lim[(3n^2+cn+1-4bn^2)/(bn)]
则3-4b=0 即b=3/4
再化成lim[(4/3)*(cn+1)/n]=4c/3=5
则c=15/4
即a=0 b=3/4 c=15/4
则-4a=0 即a=0
极限化成lim[(3n^2+cn+1-4bn^2)/(bn)]
则3-4b=0 即b=3/4
再化成lim[(4/3)*(cn+1)/n]=4c/3=5
则c=15/4
即a=0 b=3/4 c=15/4
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