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.
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)={9−x5:x=5:x=5
We know that from the limit definition: ifx→5limf(x)=4thenit is true that
ifε>0 then ∃δ>0 such that ifx∈(5−δ,5)∪(5,5+δ)then∣f(x)−4∣<ε.
What do the example & the definition have to do with the three options?
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