Question

Let f be the function defined above. Which of the following statements about f are true?

Answer 1

f(x)= (x^2 - 4)/(x-2) if x cannot equal 2
1 if x = 2

Answer 2

I. f has a limit at x = 2
II. f is continuous at x = 2
III. f is differentiable at x = 2

Answer 3

I know II. is untrue :)

Answer 4

@electrokid

Answer 5

@agent0smith

Answer 6

step 1) find the left hand side limit
step 2) find the right hand side limit.

show, then we proceed

Answer 7

idk what you mean

Answer 8

to check if the limit exists, we have to check the right hand side and the left hand side limits (one sided limits)

Answer 9

\[\Large{\text{left hand side limit:}\lim_{x\to2^-}f(x)\\
\text{right hand side limit:}\lim_{x\to2^+}f(x)
}\]

Answer 10

so in this case x^-4/(x-2) f does not have a lim at x=2

Answer 11

why not?

Answer 12

so it does exist?

Answer 13

why does it? :D
we have to check...
we first have to find the individual left hand side and right hand side limits

Answer 14

left hand side -> x comes close to 2 but is less than 2
right hand side -> x comes close to 2 but is greater than 2