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Doesn't solving limits by substituting values defeat the point? For example: you can solve a limit of a quadratic by just subbing in a x value. But how do we know limit as x approaches a is the same as f(a)?
The purpose of calculating limits by subbing in values is to determine the behavior of a function at a specific point, also known as the limit point. This allows us to understand how a function approaches a certain value and can help us make predictions about the function's behavior.
To calculate limits by subbing in values, we simply plug in values that are close to the limit point on both sides of the function. We then observe the resulting outputs and determine if they approach a specific value or if they approach infinity. This can be done by hand or with the help of a graphing calculator.
Calculating limits by subbing in values may not always give us an accurate answer, especially when dealing with more complex functions. This method only gives us an approximation of the limit and may not work for functions that have discontinuities or vertical asymptotes.
No, we cannot always use this method to calculate limits. It is only applicable when dealing with functions that are continuous at the limit point. If a function has a jump or a hole at the limit point, we cannot use this method to calculate the limit.
To check if the limit calculated by subbing in values is correct, we can use other methods such as the algebraic method, the graphing method, or the squeeze theorem. These methods can help us verify the limit and ensure that our calculation is accurate.