Question

What is the value of `lim_(x rarr 0) a`, where `a` is a constant ?

Answer 1

`lim_(x rarr 0) a = a AA a in RR\ \ \ `, where `a` is a constant

Explanation:

We seek:

`lim_(x rarr 0) a \ \ \ `, where `a` is a constant

We note that if we define a function `f` by:

`f(x) =a`

Then as `a` is a constant, it is completely independent of the variable `x`, and is continuous over the entire domain `RR`. If we examine the behavior of `f(x)` then just to the left of `x=0` then `f(x)=a`, similarly to the right, and also at `x=0` we have `f(x)=a`.

So we have:

`lim_(x rarr 0^-) f(x) = lim_(x rarr 0^+) f(x) = lim_(x rarr 0) f(x) = a`

Hence

`lim_(x rarr 0) a = a AA a in RR\ \ \ `, where `a` is a constant