what is the value of the function

[puneet bansal]

wat is the value of the function f(x)=√(4-x) if x tends to 4.
domain of this function is(-∞,4].:idea:

 

[shiv_emf]

zero

left hand limit exist in tht range as .. it is +ve number inside square root
if range gos beyond 4 .. limit does not exist....

 

[mkhan]

Hi,

Its zero, because even if you differentiate the function and apply limits then, you will get zero as x tends to 4.

Arif

 

[neils_arm_strong]

zero.
why did you ask?

 

[bangash]

zero
come on use some portion of your brain

 

[Phrzby Phil]

a limit exists only if it exists and is the same from both directions

 

[pmonon]

The limit is simply non existant as x->4, it is not zero and nothing.

 

[shiv_emf]

The limit is simply non existant as x->4, it is not zero and nothing.

plz check the limit in given range!! ..if range is nt given then ur explaination is valid

Limit does exist n its value is ZERO

Shiv

 

[pmonon]

The limit is simply non existant as x->4, it is not zero and nothing.

plz check the limit in given range!! ..if range is nt given then ur explaination is valid

Limit does exist n its value is ZERO

Shiv

Ok, you are talking about the domain? Yes. You are correct. Sorry, I missed it.

Yes, lim = 0.

 

[Phrzby Phil]

But x cannot approach 4 from the right (domain is closed at 4 at the top), so how can the limit even exist?

 

[pmonon]

But x cannot approach 4 from the right (domain is closed at 4 at the top), so how can the limit even exist?

The RH limit is the same as f(4) which equals LH limit, that is zero.

 

[tzushky]

There is no right hand limit in this case, only the left hand limit which is equal to the value in f(4) =0 ... Do not look for more, the definition of a limit existing when both sides are equal is not universal, such functions with bounded domain only have RH or LH limits and that's it...

 

[shiv_emf]

in case range is not including 4 then limit exists ..

@tzushky is correct
Shiv

 

[Phrzby Phil]

What does the range including 4 have to do with it?

 

[tzushky]

Maybe the idea was that even for (-infinity, 4) ( not including 4) the limit still exists, which is true...

There are two limits always:

lim (x->4 from left) (f(x)) and
lim (x->4 from right)(f(x))

The definition says that if those limits are equal AND also equal to the value of f(4) (IF THEY EXIST: if 4 is in the domain of the function, if a limit to right or left can be wriiten...) THEN we can say f has a limit in 4 and it is f(4). Otherwise they are still called the RH and LH limit, and they still exist...

 

[Phrzby Phil]

f(4) need not exist, and if it does it need not = the RH and LF limits.

 

[shiv_emf]

if u say f(4) exist then
f(4-) and f(4+) must exist...

 

[marko_benigno]

Hi,

Its zero, because even if you differentiate the function and apply limits then, you will get zero as x tends to 4.

Arif

Agree with this. You need to differentiate it to get the slope or where its tending the apply the boundary conditions. In this case, its zero.

 

[irfankundi]

the limit doesn't exist.

 

[shiv_emf]

the limit doesn't exist.

not again !!