Question

Calculus

Answer 1

\[\lim_{x \rightarrow 2} \frac{ \left| x - 2 \right| }{ x - 2 }\]

Answer 2

the limit will be different for x approaching 2 from above and that for x approaching 2 from below. Because the numerator will always be positive ( absolute value)

Answer 3

Limits are not my strong point I'm afraid

Answer 4

My guess is that the limit is 1 for x approaching above 2 , and -1 for x approaching from below 2. But i'm not sure.

Answer 5

That's what the calculator I used says, I just don't know how to show my work for it.

Answer 6

May not be your strong point, however you are correct @welshfella :)

As you said, the limit = -1 as we approach 2 from the left
And the limit = 1 as we approach 2 from the right

Since there are 2 different values, the limit does not exist

Answer 7

Right - i cant help you there.

Answer 8

Its easy to show,

Instead of putting in 2 for 'x'

Plug in 1.99999 for 'x' to show what the answer would be if we approach 2 from JUST below it

And plug in 2.00001 for 'x' to show what it would be if we approach 2 from JUST above it

Answer 9

- yes - I had something like that in my mind also.

Answer 10

Thank you both!