For a function to begin to qualify as differentiable, it would need to be continuous, and to that end you would require that 
is such that
Obviously, both limits are 0, so 
is indeed continuous at 
.
Now, for to be differentiable everywhere, its derivative 
must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:
and at this time, we don't know what's going on at , so we omit that case. We want to be continuous, so we require that
from which it follows that 
.
Answer:
The allowable lengths of pipe is from 21.78 inch to 22.22 inch.
Step-by-step explanation:
The length of the each pipe in the shipment = 22 inch
The variation in the length of pipes = 1%
⇒The allowable length of pipe in the inspection = 22 inch ± 1%
Now, 1% of 22 = 
So, 22 inch + 1% = 22 inch + 0.22 = 22.22 inch
and 22 inch - 1% = 22 inch - 0.22 = 21.78 inch
⇒ 22 inch ± 1% = 22.22 inch and 21.78 inch
Hence, the allowable lengths of pipe is from 21.78 inch to 22.22 inch.
Answer:
c
Step-by-step explanation:
just substitute a big number into x like 10^6 as it approaches
and a big negative number like -10^6 as it approaches
The answer to the equation is x < 2.
