What is the volume, in cubic m, of a rectangular prism with a height of 15m, a width of 4m, and a length of 13m?
1 answer:
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Answer:
If whenever
f is <em>increasing</em> on I.
If whenever
f is <em>decreasing</em> on I.
Step-by-step explanation:
These are definitions for real-valued functions f:I→R. To help you remember the definitions, you can interpret them in the following way:
When you choose any two numbers on I and compare their image under f, the following can happen.
. Because x2 is bigger than x1, you can think of f also becoming bigger, that is, f is increasing. The bigger the number x2, the bigger f becomes.
. The bigger the number x2, the smaller f becomes so f is "going down", that is, f is decreasing.
Note that this must hold for ALL choices of x1, x2. There exist many functions that are neither increasing nor decreasing, but usually some definition applies for continuous functions on a small enough interval I.
For 
to be continuous at 
, we need to have
Note that
means that 
, but that 
is *approaching* 5. We're told that for , we have
We can write
and the limit would be
and so is discontinuous.
Note that
We can write
and the limit would be
and so