- #1
j-lee00
- 95
- 0
The problem is not to conduct the proof but how the proof works. (It seems to be a circular argument)
Please use laymans english to explain, thank you
Please use laymans english to explain, thank you
The formal definition of the limit of a function is the value that the function approaches as the input (x) gets closer and closer to a specific value (a). This is denoted by the notation lim f(x) = L, where L is the limit and x approaches a.
The limit of a function is the value that the function approaches as x gets closer to a specific value. It is not necessarily the same as the value of the function at that specific point. The limit is a theoretical concept, while the value at a specific point is the actual output of the function at that point.
Limits are a fundamental concept in calculus and are essential for understanding the behavior of functions. They allow us to determine the rate of change of a function, the existence of derivatives, and the convergence or divergence of infinite series. Limits are also used in many real-world applications, such as optimization and optimization problems.
A one-sided limit is a limit where x only approaches the specified value from one side. This means that the value of the function as x approaches the specified value from the left or right may be different. One-sided limits are used when there is a discontinuity in the function or when the function is defined differently on either side of the specified value.
To calculate the limit of a function algebraically, you can use the limit laws, which state that the limit of a sum, difference, product, or quotient of two functions is equal to the sum, difference, product, or quotient of the limits of the individual functions. You can also use substitution, where you substitute the specified value into the function and simplify. However, in some cases, you may need to use more advanced techniques, such as L'Hopital's rule or the squeeze theorem, to evaluate the limit.