define what it means to say that lim x->0 g(x)=k?

Question

 define what it means to say that lim x->0 g(x)=k?

Answer 1

Aron,

I would interpret your question to say: what is the limit of g(x), as x goes to 0, if g(x) = k?

This editor isn't going to let me write it much, if any, better than you did. Anyway......

 

They are asking for the limiting value of g(x), which most often means y, when x approaches 0. The original intent of this type of statement was to lend some definition to a function which is undefined at a certain value of x. For example, the function f(x) = 1/x is undefined when x = 0. If you graph this function, you will see that coming from the right, it goes to positive ∞, while from the left, it goes to negative ∞. Since the two sides do not come to the same point, we say there is no general limit.

 

But text books generally have come to use it for any location of any function. So for example: the limit of f(x) = 3x as x approaches 2 is just 6. In other words, if it's not undefined, just plug in the number.

 

Limits can be much more complicated and truly warrant a lengthy discussion. I hope this is enough for what you need.