
这个第十题可以要具体步骤吗,我不会写,非常感谢
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(10)
let
1/y =5/(3x-1)
lim(x->∞) [ (3x+4)/(3x-1) ]^x
=lim(x->∞) [ 1+ 5/(3x-1) ]^x
=lim(y->∞) [ 1+ 1/y ]^[(5y+1)/3]
=lim(y->∞) [ 1+ 1/y ]^(5y/3)
=e^(5/3)
let
1/y =5/(3x-1)
lim(x->∞) [ (3x+4)/(3x-1) ]^x
=lim(x->∞) [ 1+ 5/(3x-1) ]^x
=lim(y->∞) [ 1+ 1/y ]^[(5y+1)/3]
=lim(y->∞) [ 1+ 1/y ]^(5y/3)
=e^(5/3)
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=e^limxln(1+5/(3x-1))
=e^limx*5/(3x-1)
=e^(5/3)
=e^limx*5/(3x-1)
=e^(5/3)
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