Question

极限x趋近于无穷(x-1/x+2)^x+1 求极限

Answer 1

猜测你漏了3个括号

[(x-1)/(x+2)]^(x+1)

=[1-3/(x+2)]^(x+1)

={[1-1/(x/3+2/3)]^(x/3+2/3)}^[(x+1)/(x/3+2/3)]

然后取极限

令t=x/3+2/3->无穷

原式=[(1-1/t)^(t)]^[(3t-1)/t]

底数的极限是e^(-1)

指数极限=3-1/t=3

所以答案是[e^(-1)]^3=e^(-3)