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找出极限lim(1+(3/x)+(5/x^2))^xx->∞
题目详情
找出极限
lim (1+(3/x)+(5/x^2))^x
x->∞
lim (1+(3/x)+(5/x^2))^x
x->∞
▼优质解答
答案和解析
lim (1+(3/x)+(5/x^2))^x
x->∞
=lim (1+（3x/x^2）+(5/x^2))^x
x->∞
=lim (1+(3x+5）/x^2))^x
x->∞
=lim (1+(3x+5）/x^2)^[x^2/(3x+5）]*[(3x+5）/x^2]*x
x->∞
=e^lim(3x+5）/x
=e^lim(3+5/x)
=e^3
x->∞
=lim (1+（3x/x^2）+(5/x^2))^x
x->∞
=lim (1+(3x+5）/x^2))^x
x->∞
=lim (1+(3x+5）/x^2)^[x^2/(3x+5）]*[(3x+5）/x^2]*x
x->∞
=e^lim(3x+5）/x
=e^lim(3+5/x)
=e^3
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