urgent help

[solver2]

Suppose lim x →5 f(x) = 4 .
Which of the following statements are true without further restrictions on f?
A. f is defined on (a, 5) ∪ (5, b) for some a < 5 < b.
B. Range of f contains 4.
C. As f(x) approaches 4, x approaches 5.

 

[yoscar04]

The are guidelines for this forum you should consult before posting a problem. Please show us what do you know and where are you stuck.

 

[pka]

Suppose lim x →5 f(x) = 4 .
Which of the following statements are true without further restrictions on f?
A. f is defined on (a, 5) ∪ (5, b) for some a < 5 < b.
B. Range of f contains 4.
C. As f(x) approaches 4, x approaches 5.

I stress that the use of example is no good for proofs, but are very good as counter-examples.
Consider:
\(f(x)=\begin{cases}9-x &: x\ne 5 \\ 5 &: x=5\end{cases}\)

We know that from the limit definition: if \(\mathop {\lim }\limits_{x \to 5} f(x) = 4\) then it is true that
if \(\varepsilon>0\) then \(\exists\delta>0\) such that if \(x\in (5-\delta,5)\cup (5,5+\delta)\) then \(|f(x)-4|<\varepsilon\).
What do the example & the definition have to do with the three options?