Question

Suppose the lim f(x)=4 as x approaches 5 Which of the following statements are true without further restrictions on f? A. f is defined on (a, b) for some a < 5 < b. B. As f(x) approaches 4, x approaches 5. C. Range of f need not contain 4.

PLEASE HELP ME.

Answer 1

as the limit exist as x--->5 thus f is defined on (a,b) containing 5 therefore the correct choice is
A. f is defined on (a, b) for some a < 5 < b

Answer 2

what about c? The range doesn't have to contain 4 right?

Answer 3

It can be more than one correct answer =/

Answer 4

you are right but if you see this is a limit from both sides means if we approach 5 from either side f(x) will become 4 so it means that f(x) is defined at x = 5. which means f(x) = 4 when x= 5.

Answer 5

Yes makes perfect sense. Thank you. Can you please explain why B is not true?

Answer 6

thats also correct no doubt.

Answer 7

i read the choice B as incorrect but that was my mistake.
its 100% correct.

Answer 8

okay thank you so A & B are correct only right

Answer 9

yesss

Answer 10

both are right and you are welcome