find lim of f(x) where f(x) is a piece wise function As follows f(x) = | x | + 1, x 0 where x is approaching a ( x - a )

Question

find lim of f(x) where f(x) is a piece wise function As follows
f(x) = | x | + 1, x < 0   
           0          , x = 0 
           | x | - 1, x > 0 
where x is approaching a   ( x -> a )

anonymous · Answer

f(x) = -x + 1,   if x < 0 
         0        ,   if x = 0
          x - 1 ,    if x > 0 
     as x approaching a

turingtest · Answer

x -> a
?
not x -> 1
?

anonymous · Answer

yah x -> a     where a is not given as some specific value just real number a

turingtest · Answer

well what is |a|+1
?

turingtest · Answer

can it ever be 0
?

anonymous · Answer

You're misreading the problem... a must be some definite number, or else infinity.

anonymous · Answer

nothing regarding this is given.

turingtest · Answer

@SmoothMath
^ is that at me or the asker

anonymous · Answer

SmotthMath... no no really that problem is without any mistake believe me

turingtest · Answer

answer my question please @jatinbansalhot

anonymous · Answer

|dw:1334241670355:dw|

turingtest · Answer

your book is wrong I think...
as SmoothMath's drawing shows

anonymous · Answer

Ah, well okay then. That's easy.
If a = 0, then the limit does not exist because the left an dright limits are not equal.
If a is not 0, then the limit will just be the result of plugging into the function.

anonymous · Answer

yah.. if a = 0 then lim doesn't exist. it is given in my book

anonymous · Answer

In other words, lim x->a = 
-(a)+1 if a<0 
a-1 if a >0

turingtest · Answer

neither imply that the limit exists

turingtest · Answer

the limit at a point $p$ exists iff$$\lim_{x\to p^+}f(x)=\lim_{x\to p^-}f(x)$$

anonymous · Answer

good then plz ...

anonymous · Answer

Look at the point a=0, and think about approaching it from the right. As x values get close to 0, what do the y values approach?
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