lim{(2+3x)/(3+3x)}x次方,x趋于无穷,求极限,麻烦写过程,

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 23:05:27
lim{(2+3x)/(3+3x)}x次方,x趋于无穷,求极限,麻烦写过程,

lim{(2+3x)/(3+3x)}x次方,x趋于无穷,求极限,麻烦写过程,
lim{(2+3x)/(3+3x)}x次方,x趋于无穷,求极限,麻烦写过程,

lim{(2+3x)/(3+3x)}x次方,x趋于无穷,求极限,麻烦写过程,
原式=lim{1+(1/-(3+3x))}^{(-(3+3x))*[x/(3+3x)]}=lime^(-x/(3+3x))=lime^(-1/(3+3/x))=e^(-1/3)
"^"表示次方 ,

lim(x->无穷){(2+3x)/(3+3x)}^(x)
= lim(x->无穷) [1-1/[3+3x)]^(x)
let y = 3+3x
lim(x->无穷) [1-1/[3+3x)]^(x)
=lim(y->无穷) [1-1/[y)]^((y-3)/3)
=lim(y->无穷) [1-1/[y)]^((y/3) .lim(y->无穷) [1-1/[y)]^(-1)
= e^(-1/3). 1
=e^(-1/3)

lim{(2+3x)/(3+3x)}x次方
=lim{(3+3x-1)/(3+3x)}x次方
=lim(1-1/(3x+3))x次方
=e^lim(-x/(3x+3))
=e^(-1/3)

当x趋于无穷时,(2+3x)/(3+3x)则趋于1,{(2+3x)/(3+3x)}x次方相当于1的x次方,则为1.