Question

f(x)= -x^2+2, 0≤ x <1
2, x=1
x^2, 1 12 years ago

Answer 1

how far did you get?

Answer 2

i think a) is 4 but I am not sure

Answer 3

a) is 4, nice work

Answer 4

you start on the left side of x = 2, then you slowly approach x = 2 along the graph and you'll get closer and closer to y = 4

Answer 5

how about b?

Answer 6

Idk how to do b :/

Answer 7

what is the limiting value of f(x) as x ---> 1

Answer 8

ie if you approach x = 1 from both directions, what does y get closer and closer to?

Answer 9

2?

Answer 10

no you approach x = 1

this means you get closer and closer to x = 1...but you actually never officially arrive at x = 1

Answer 11

does that make sense?

Answer 12

yes

Answer 13

what about f(1)?

Answer 14

f(1) is the y value of the point at x = 1

Answer 15

the limit is slowly approaching x = 1 (it never gets there officially, just gets closer and closer)

f(1) is actually at x = 1 (it's officially there and stopped)

Answer 16

so f(1) has a greater value

Answer 17

good, the limiting value as x ----> 1 is 1

but f(1) = 2

so you are correct

Answer 18

idk how to do c:/

Answer 19

what are some points where the limit does not exist?

Answer 20

where the holes are at, i think

Answer 21

that's a good guess, but look how the limit exists at x = 1

this is because you can approach x = 1 from either side and arrive at the same y value

Answer 22

however, the limit does NOT exist at x = 2, why is this?

Answer 23

cause the lim f(x) as x approaches 2- is 4 and the lim f(x) as x approaches 2+ is 3 so limf(x) as x approaches 2 does not exist because those two limits aren't equal

Answer 24

bingo

Answer 25

the left and right hand limits are NOT equal, so the limit does NOT exist

Answer 26

what's another point where the limit doesn't exist?

Answer 27

I am not sure :/

Answer 28

hint: it's not in the middle

Answer 29

wait so the limit f(x) as x approaches 2, does not exist, is part of my answer?

Answer 30

yes, there's another point though

Answer 31

c = 2 is one value

but there is one more value of c

Answer 32

is it c=0

Answer 33

yep, the limit does NOT exist at x = 0

Answer 34

because the left hand limit does not exist

Answer 35

both the left and right hand limits must exist and they must be equal for the overall limit to exist

Answer 36

why doesn't the left hand limit exist?

Answer 37

because the function ends at x = 0, so there is no bit to the left to start approaching from

Answer 38

the general rule is that the limit does not exist at endpoints because you can't approach from beyond the function

Answer 39

ooh okay got it:)

Answer 40

that's great

Answer 41

thank you:)

Answer 42

you're welcome