What is the limit as x approaches infinity of a constant? Is it the constant or zero?
Thanks in advance!
since a constant does not depend on x, its value does not change no matter what x does.
When a constant function is evaluated as x approaches infinity, the limit is equal to the constant itself. In other words, if the function f(x) is a constant c, then the limit as x approaches infinity of f(x) is c. It is not zero.
The limit of a constant as x approaches infinity is simply the constant itself. In other words, if you have a constant "c" and you take the limit as x approaches infinity, the value of the function will always be "c".
To understand why this is the case, let's go through the definition of a limit. In calculus, the limit of a function as x approaches infinity means that we're interested in understanding the behavior of the function as x gets larger and larger without bound.
Now, when we're dealing with a constant, it means that the function doesn't change as x changes. So, no matter how large x gets, the function always returns the same constant value. As a result, the limit of the constant as x approaches infinity is simply the constant itself.
To calculate the limit of any function as x approaches infinity, you need to check if it falls into any of the categories that have specific limit values (e.g. constants, polynomials, exponential functions, etc.). In the case of a constant, you can conclude that the limit is the constant itself.
I hope this explanation helps! If you have any more questions, feel free to ask.