Complete Question
1 Explain what is meant by the equation lim x → 8 f(x) = 9.
A If |x1 − 8| < |x2 − 8|, then |f(x1) − 9| < |f(x2) − 9|.
B The values of f(x) can be made as close to 8 as we like by taking x sufficiently close to 9.
C f(x) = 9 for all values of x.
D If |x1 − 8| < |x2 − 8|, then |f(x1) − 9|≤ |f(x2) − 9|.
E The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 8.
2 Is it possible for this statement to be true and yet f(8) = 6? Explain.
A Yes, the graph could have a hole at (8, 9) and be defined such that f(8) =6.
B Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 6.
C No, if f(8) = 6, then lim x→8 f(x) = 6.
D No, if lim x→8 f(x) = 9, then f(8) = 9.
Answer:
1
The correct option is D
2
The correct option is A
Step-by-step explanation:
Generally a a limit function [tex]\lim_{n \to x } f(x) = L[/tex]
Tell us that as n tends toward x the values of f(x) tends towards L hence for the first question E is the correct option
Now looking at the second question
Yes it is possible for lim x → 8 f(x) = 9. to be true and f(8) = 6 this is because the graph defined by this limit equation can have a hole the point
(8, 9) and created in such a way that f(8) = 6
