what is the value of the function

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puneet bansal

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

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....
 

Hi,

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

Arif
 

zero
come on use some portion of your brain
 

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

pmonon said:
The limit is simply non existant as x->4, it is not zero and nothing.
Click to expand...

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.
 

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

Phrzby Phil said:
But x cannot approach 4 from the right (domain is closed at 4 at the top), so how can the limit even exist?
Click to expand...
The RH limit is the same as f(4) which equals LH limit, that is zero.
 

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...
 

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

@tzushky is correct
Shiv
 

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...
 

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

mkhan said:
Hi,

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

Arif
Click to expand...

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.
 

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