Question

Find the indicated limit, if it exists.

limit of f of x as x approaches 1 where f of x equals 1 minus x when x is less than 1, 8 when x equals 1, and x plus 7 when x is greater than 1

Answer 1

what do you think?

Answer 2

The answers are:
8
0
7
The limit does not exist.

I think the answer is 8. Is that correct?

Answer 3

@freckles

Answer 4

hmmm just take the limit to the right of 1 and also limit to the left of 1

Answer 5

and then compare if they are equal

Answer 6

good job @xapproachesinfinity @sunshine201

Answer 7

so first start with \(\large \lim_{x\to1^{+}}f(x)=\lim_{x\to1^{+}}x+7=?\)

Answer 8

8?

Answer 9

correct! how about the left

Answer 10

Is that the one that's 1 - x?

Answer 11

yes x<1 means we are taking number to the left of 1

Answer 12

so 1 - 8 = -7?

Answer 13

hmmm no
we are doing the limit to the left of 1

Answer 14

so you have to evaluate 1 not 8

Answer 15

\(\large \lim_{x\to1^{-}}1-x=?\)

Answer 16

1 - 1 = 0?

Answer 17

you got it?

Answer 18

The limit is 0?

Answer 19

yes correct! now is this true \(\large \lim_{x\to1^{+}}f(x)=\lim_{x\to1^{-}}f(x)\)

Answer 20

for the limit to exist the two limits must equal

Answer 21

we are looking for the limit as x goes to 1
so we need to test the limit from the right and the limit from the left of 1
and then compare

Answer 22

limit from the right is 8
limit from the left is 0
what can you say

Answer 23

what do you think

Answer 24

@bohotness