Find Lim f(x) as x->0
for
f(x)=5x-8 ......x<0
f(x)=|-4-x|......x ≥ 0
Clearly
f(0)=|-4-0|=|-4|=4 exists.
The left-hand limit, as x-> 0- is f(0-)=5(0)-8=-8
The right hand limit, as x->0+ is f(0+)=|-4-0|=|-4|=4
Since the left and right limits do not both equal f(0), the limit does not exist.
Answer:
The limit does not exists.
Step-by-step explanation:
Given:
f(x) = 5x - 8 ; x < 0
f(x) = l -4 -x l ; x ≥ 0
Now we have to find the limit when x approaches to 0.
Condition:
If the left hand limit is equal to the right hand limit, then only the limit exists.
Now let's find the left hand limit.
lim 5x - 8
x ---> 0
Now let's apply the limit x = 0, we get
5(0) - 8 = -8
The left hand limit is -8
Now let's find the right hand limit.
lim l -4 - x l
x ----> 0
Now plug in x = 0 in the above absolute function, we get
l -4 - 0 l = l -4 l = 4 [Absolute value of a negative number is positive]
The right hand limit is 4.
Here we can see that the left hand limit does not equal to the right hand limit.
Therefore, the limit does not exists.
