Question

The lim h->0 abs(x+h)-abs(x)/h at x=3 is?

Answer 1

can i see a pic of you, i will answer your question

Answer 2

uhm a pic of me?

Answer 3

1

Answer 4

yeah

Answer 5

why?

Answer 6

it helps me do math

Answer 7

keeps my mind on the prize,

Answer 8

if x>0 then |x+h|=x+h and |x|=x
if x<0 then |x+h|=-(x+h) and |x|=-x
but we have the first version so the answer is 1

Answer 9

so i don't put 0 in for h?

Answer 10

h/h=1

Answer 11

the derivative is not defined for absolute value at x = 0

Answer 12

oh but near x = 3, thats fine

Answer 13

right the answer is 1

Answer 14

By the definition of a derivative, this is derivative of lxl at x=3. Don't you agree myininaya?

Answer 15

look at the graph of y = | x|

Answer 16

its a V, it has two branches , the negative branch has slope -1, the positive branch has +1 slope

Answer 17

bur since there is a sharp turn at x=0 then f' dne at x=0

Answer 18

so for all x>0 f'(x)=1
for all x<0 f'(x)=-1
f'(0) DNE

Answer 19

Yeah, I agree.

Answer 20

yeah we agree on something lol

Answer 21

:)

Answer 22

anwar, i proved the lim problem

Answer 23

You did?

Answer 24

its a direct result of using the definition of a limit

Answer 25

yeah

Answer 26

How?

Answer 27

You did it or someone did it and you claimed it's you, as you did with mine? :P

Answer 28

well someone said to state the definition of a limit

Answer 29

and then i looked at it, and voila

Answer 30

I see. Btw, I was just kidding.

Answer 31

oh i see, dark humor

Answer 32

LETS do the proof