A limit in mathematics represents the value that a function approaches as the input value gets closer and closer to a specific value.
To find the limit of a function, you need to substitute the value that the function is approaching into the function and evaluate the result. You may also use algebraic manipulation or graphing to determine the limit.
The limit of the given function is undefined. This is because the function is undefined at x = 2 and x = -2, and as x approaches these values, the function becomes undefined.
The limit of a function can be proven using the epsilon-delta definition, where you can show that for any small value of epsilon, there exists a corresponding value of delta that will make the distance between the limit and the function value less than epsilon.
Finding the limit of a function is important in calculus and other areas of mathematics as it helps us understand the behavior of a function near a specific input value. It also allows us to determine key properties of a function, such as continuity and differentiability, and can be used to solve more complex problems in mathematics and science.