Question

How do I find the limit of x/x-4 as x->4 without plugging in numbers close to 4?

Answer 1

If its \[\lim_{x\rightarrow 4}{\frac{x}{x-4}}\]
Then the answer is undefined! as in the answer is standard for a reciprocal question:
\[\lim_{x\rightarrow 4^+}{\frac{x}{x-4}}=\infty\phantom{pad to next question}\lim_{x\rightarrow 4^-}{\frac{x}{x-4}}=-\infty\]
But if it's:
\[\lim_{x\rightarrow4}{\left[\frac{x}{x}-4\right]}\]
Then in general:
\[\lim_{x\rightarrow a}{\left[\frac{x}{x}-4\right]}=-3\]

Answer 2

It's the first one. How do I show that it is infinite from the right or from the left without plugging in numbers?

Answer 3

Erm...without numbers...hmm

Answer 4

Im not quite sure to be honest, I wouldn't want to lie haha

Answer 5

Alright, thanks anyway!