Question

求极限问题 洛必达

Answer 1

原式 = lim<x→0>(xe^x + x - 2e^x +2)/x^3 (0/0)
= lim<x→0>[(x+1)e^x + 1 - 2e^x]/(3x^2) (0/0)
= lim<x→0>[(x+2)e^x - 2e^x]/(6x)
= lim<x→0>e^x/6 = 1/6

Answer 2

让我们万能的matlab 来解脱你
close all; clear; clc;
syms x
y = (x*(exp(x)+1)-2*(exp(x)-1))/(x*sin(x)^2);
result = limit(y,x,0);
结果是 1/6