Question

when i have a limit of x going towards 0 do i still plug 0 into the equation?

Answer 1

Do you have a specific example?

Answer 2

Depends on the problem. If you're dealing with a rational function and you have the factor x in the denominator, no, you cannot just plug in 0 because you'd end up with div. by 0.

Answer 3

J-Dawg?

Answer 4

@jdogw, that really depends on the level of studying you're currently at. At a very naive point of view I would yes, yes go for it, plugin \(x=0\) into the equation, from a rigorous mathematical point of view you cannot do that, consider the definition of a limit of a function.
Let \(f: E \to F\) be a function where \(E \subset \mathbb{R}^m\) and \(F \subset \mathbb{R}^n\) and let \(a \in \mathbb{R}^m\) then we write \[\lim_{x \to x_0}f(x)=a \iff \forall \epsilon > 0, \exists \delta > 0 \text{ s.t. } \forall x \in E , (0 < d(x,x_0)< \delta \to d(f(x),a) < \epsilon)\]
So considering this more rigorous definition of what a limit is, you cannot plugin \(x=x_0\) because that would imply that \(0 < 0\) which is clearly a contradiction. More intuitively, you can plugin values that get closer and closer (infinitesimal) close to \(x_0\).