Find the indicated limit, if it exists. limit of f of x as x approaches 0 where f of x equals 5 x minus 8 when x is less than 0 and the absolute value of the quantity negative 4 minus x when x is greater than or equal to 0

Find Lim f(x) as x->0

for

f(x)=5x-8 x<0

f(x)=|-4-x|x &ge; 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.

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