Question

What is the limit as x approaches infinity of a constant?

Answer 1

In order to solve this problem, we need to be clear with our concepts of limits. We should understand what limit of a function actually means. Having known this, we can move forward to conclude what is the limit as x approaches infinity of a constant.

Complete step-by-step answer:
In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit of a function is usually written as
$\displaystyle \lim_{x \to c}f\left( x \right)=L$
and is read as "the limit of $f$ of x as x approaches c equals L". The fact that a function f approaches the limit L as x approaches c is sometimes denoted by a right arrow.
Now, the limit of a constant is something interesting. A constant function always remains a constant since it is independent of the value of any variable. The value of a constant remains constant no matter what the variable value tends to or approaches to.
Thus, we can conclude that the limit as x approaches infinity of a constant is the constant itself.

Note: These types of problems where we are asked to find a limit of a function create a confusion among students. But, if we have a clear understanding, the confusion can be got rid of. Students also make a mistake of writing the answer to the problem as zero. We should try to avoid them.