Aviegaille said:
The limit of a function f(x) as x approaches a is the value that f(x) approaches as x gets closer and closer to a, but may not necessarily be equal to at a.
To evaluate a limit, you can use algebraic manipulation to simplify the expression until you can directly substitute the value of the limit into the simplified expression. In this case, you can use properties of exponents to simplify the numerator, and then factor out the common h in the denominator.
Evaluating a limit allows us to find the behaviors of a function as x approaches a certain value. It can help us determine if a function is continuous or discontinuous at a specific point, and is an important concept in calculus and other areas of math and science.
Yes, a limit may not exist if the function has a vertical asymptote or if the left and right-hand limits approach different values. In this case, the limit is said to be undefined.
You can evaluate a limit using the graph of a function by finding the y-value of the point on the graph that corresponds to the limit's value. This is the value that the function approaches as x approaches the given value. Alternatively, you can also use the graph to estimate the limit by looking at the behavior of the function near the given value.
