Limit in mathematics is one of the basic concepts of calculus, which describes the trend of a function at a certain point or at infinity. Here are some classic limit examples:

1. Found $lim_{xto0}frac{sinx}{x}$. This is a famous limit problem, and its answer is 1. This problem can be solved by L'H?pital's law or Taylor series.

2. Find $ lim _ {xto infty} left (1+frac {1} {x} right) x $. The answer to this question is e, which can be solved by Taylor series.

3. Find $ lim _ {xtoa} frac {x n-a n} {x-a} $. The answer to this question is na {n- 1}. This problem can be solved by L'H?pital's law.

4. Find $ lim _ {xtoinity} sqrt {x 2+x}-x $. The answer to this question is $frac{ 1}{2}$. This problem can be solved by L'H?pital's law.

5. Find $ lim _ {xtoa} frac {ex-e {-x}} {x-a} $. The answer to this question is 2e. This problem can be solved by L'H?pital's law.

These examples are all classical questions about limit, covering the basic concepts and solutions of limit. By solving these problems, we can better understand the concept of limit and master the solution method of limit.