Question

lim(1 1/x)∧x²/e∧x用e抬起算x趋向于无穷的极限怎么算

Answer 1

lim(x→1-) [(x2-1)/(x-1)]e^[1/(x-1)]=lim(x→1-) (x+1)e^[1/(x-1)]=0 lim(x→1+) [(x2-1)/(x-1)]e^[1/(x-1)]=lim(x→1+) (x+1)e^[1/(x-1)]→+∞ ∵lim(x→1-) [(x2-1)/(x-1)]e^[1/(x-1)]≠lim(x→1+) [(x2-1)/(x-1)]e^[1/(x-1)] ∴极限lim(x→1) [(x2-1)/(x-1)]e^[1/(x-1)]不存在，但不为无穷大 C和D的区别在于C是指左极限和右极限都趋于无穷大，但D是左极限不等于右极限