Question

f(x) = | x |
find lim of f at x = 0

Answer 1

can you help me plz ?

Answer 2

0, draw the graph. Or use the Left hand limit = right hand limit test.

Answer 3

you mean to say that.. limit at x = 0 exits?

Answer 4

does derivative at x = 0 exit?

Answer 5

Yes and No.

Answer 6

yes and no ............... i didn't understand ? so confused....

Answer 7

ohhhhhhhhhhh now i got u

Answer 8

yes means limit exists and no means derivative don't know

Answer 9

Limit exists at x->0 but derivative is not defined at x=0

Answer 10

limit is zero

Answer 11

Experiment... i have some confusion... regarding derivative..

Answer 12

in my book it is said that f don't have derivative at x = 0 if at x =0 limit doesn't exits? what does it mean ?

Answer 13

derivative is related to slope, while limit is related to value

Answer 14

but derivative is also a limit value

Answer 15

derivative is limit value of slope
limit is limit value of function itself.

Answer 16

ohhh.... that is point of differentiability ?

Answer 17

that = what

Answer 18

what is point of differentiability ?

Answer 19

"f don't have derivative at x = 0 if at x =0 limit doesn't exits" <-- this is untrue

for derivative to exist => limit must exist

for limit to exist => not necessary that derivative must exist.

Answer 20

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh now i got .... thanks a lot alot .... :).... that is true but conversely not true..................:) thanks experiment :)

Answer 21

sorry "f don't have derivative at x = 0 if at x =0 limit doesn't exits" <-- this is untrue" <--- this is true ... i misread question.

Answer 22

IS IT TRUE that if derivative at x = 8 exists then lim at x = 8 also exists ?

Answer 23

*i misread statement.

Answer 24

yes ... if derivative exist, then limit must exist .... if limit exist then not necessarily derivative must exist. the above function is an example.

Answer 25

now everything is clear .... :) :) :) :) thanks Experiment .. :)... i will come back with new problem.. :) if any ............

Answer 26

k you are welcome.