hpthinker said:Yes so if I multiplied top and bottom by 5. I would get 5sin(x) / 5x - 5 [tex]\pi[/tex] wouldn't that give me something like 5/-5[tex]\pi[/tex] ?
A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It represents the value that a function is approaching, rather than the actual value at that point.
To evaluate a limit, you can use various techniques such as substitution, factoring, and algebraic manipulation. You can also use the properties of limits, such as the sum, difference, product, and quotient rules, to simplify the expression and find the limit.
A one-sided limit only considers the behavior of a function as its input approaches from one direction, either from the left or the right. In contrast, a two-sided limit considers the behavior of a function as its input approaches from both directions.
Yes, a limit can exist even if the function is undefined at that point. For example, the limit of the function f(x) = 1/x as x approaches 0 exists, even though the function is undefined at x = 0.
Limits are important in mathematics because they allow us to define and analyze the behavior of functions, particularly at points where the functions may not be defined. They are also essential in the development of calculus, as they are used to calculate derivatives and integrals.