Question

根据函数极限的定义证明

图上第三题

Answer 1

用定义证明极限都是格式的写法，依样画葫芦就镇袭是：任意给定ε>0，要使 |(1+x3)/困带(2x3)-(1/2)| = (1/2)|1/x3| ε，只须 |x| > 1/[3√(2ε)]，取 X = 1/[3√(2ε)]> 0，则当 |x| > X 时，就有 |(1+x3)/(2x3)-(1/2)| = (1/御尺兄2)|1/x3| < (1/2)(1/X3) = ε，根据极限的定义，得证。