- #1
bobsmith76
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If you look at this text towards the very end they are dividing by 2. I don't see why.
The precise definition of limits in calculus is the value that a function approaches as the input (x-value) approaches a certain value. This means that the output (y-value) of the function gets closer and closer to a particular number as the input gets closer and closer to a specific value.
The limit of a function is the value that the function approaches as the input gets closer and closer to a certain value. This value may or may not be the same as the value of the function at that specific point. The limit focuses on the behavior of the function near a specific input, while the value of the function at a point is the actual output of the function at that point.
A limit does not exist when the function does not approach a single, finite value as the input approaches a certain value. This can happen if the function has a jump or discontinuity at that point, or if the outputs of the function get increasingly larger or smaller without approaching a specific value.
To calculate a limit using the precise definition, you must first determine the value that the input is approaching. This could be a specific number, infinity, or negative infinity. Then, you must use the limit definition formula and plug in the value of the input, as well as the function itself. Lastly, you must simplify the resulting expression and see if it approaches a specific value as the input gets closer and closer to the desired value.
Understanding the precise definition of limits is crucial for understanding the behavior of functions and their outputs near specific points. It is also essential for understanding more advanced concepts in calculus, such as derivatives and integrals. Additionally, the concept of limits is widely used in many areas of science and engineering, making it an important foundational concept to grasp.