Limit: Lim {(2x + SiNx) / X} (x - > infinity) The answer to this question is to divide the fraction into 2 + (SiNx / x) and find its limit as 2, But I use the law of Robida to seek the upper and lower derivatives, the limit is 2 + LIM (cosx) (x - > infinity), and the result is not 2. Why is the result different from the answer? Is it my fault? The original formula is infinity / infinity, and there is nothing wrong with the law of Robida?

Limit: Lim {(2x + SiNx) / X} (x - > infinity) The answer to this question is to divide the fraction into 2 + (SiNx / x) and find its limit as 2, But I use the law of Robida to seek the upper and lower derivatives, the limit is 2 + LIM (cosx) (x - > infinity), and the result is not 2. Why is the result different from the answer? Is it my fault? The original formula is infinity / infinity, and there is nothing wrong with the law of Robida?

When X - > infinity, 1 / X - > 0, that is to say, 1 / X is an infinitesimal, and SiNx is bounded (range is [- 1,1]), the infinitesimal multiplied by a bounded function equals