急求lim(x趋向无穷)(2x-1/2x+3)^x-1
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急求lim(x趋向无穷)(2x-1/2x+3)^x-1
急求lim(x趋向无穷)(2x-1/2x+3)^x-1
急求lim(x趋向无穷)(2x-1/2x+3)^x-1
解
求极限x➔∞[(2x-1)/(2x+3)]^(x-1)
原式=x➔∞[1-4/(2x+3)]^(x-1);令-4/(2x+3)=u,则x=-(3/2)-(2/u),x➔∞时u➔0;代入原式得:
原式=u➔0(1+u)^(-5/2-2/u)=u➔0[(1+u)^(1/u)]⁻²[(1+u)^(-5/2)]=e⁻²=1/e²
急求lim(x趋向无穷)(2x-1/2x+3)^x-1
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