Question

is it necessary to take the limit of continuous functions always?

Answer 1

i believe it is important

Answer 2

is the question whether you need to take the limit or whether the function needs to be continuous?

Answer 3

Though im not completely sure.

Answer 4

then why we say that function is not defined at that point.

Answer 5

can you tell me what you are referring to?

Answer 6

in every definition of limit we read the same thing

Answer 7

if you answer my question i can answer yours

Answer 8

which is simply to clarify please

Answer 9

I agree with Euler271. Witch are you talking about.?

Answer 10

@euler when we read the def of limit it starts with ''let f be a function defined everywhere in the interval I except possibly at x=a and then we say lim f(x)=L. i want to know that why function is not defined that point.
x->a

Answer 11

and for a continuous function i asked in general not for a particular que.

Answer 12

every function that has at least one point where it is undefined is not continuous

Answer 13

it means limit is not taken for continuous function

Answer 14

not continuous means that some value of x makes for an "illegal operation". for example f(x) = 1/(x-1) is undefined at x=1 since it would = 1/0. f(x) = 2x is continuous, for example.

you can still take the limit of this function.

you can take the limit of every function :).

Answer 15

so we would say f(x) = 1/(x-1) is discontinuous at x =1.

Answer 16

but how can we take the limit of f(x) = 1/(x-1)

Answer 17

as x->1

Answer 18

you would need to find

lim x-> 1(-) as well as lim x->1(+)

which translate to as x approaches 1 from the left and as x approaches 1 from the right.

let me find my calculus notes to remember how eactly to do that :P

Answer 19

ok but please reply quickly

Answer 20

ya you would write is as

if x<1 lim = -inf
if x>1 lim = +inf

Answer 21

and since they are not the same, it is undefined in this case

Answer 22

which on a graph would look like vertical asymptotes at x=1

Answer 23

but we have to put values close to 1 from both L.H.S and R.H.S isn't it?

Answer 24

yes. it can be done by hand since sometimes it converges to a number but notice by calculator that 1/(1.00000000000000000000000000000000000000000001 - 1) = a larger number, the closer you get.

Answer 25

then why u say if x<1 lim = -inf if x>1 lim = +inf?

Answer 26

because 1/(0.99999999999999999999 -1) is a negatively large number. by googling the function you can see what it looks like at x=1:

https://www.google.com/search?q=1%2F%28x-1%29&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official

Answer 27

ok thanks

Answer 28

np. id be glad to answer any other questions :)

Answer 29

lol y u no give medal? :P

Answer 30

I'll give you one. :)

Answer 31

:) ty