Enter two numbers to check if the first number is divisible by the second number: Check
Problem:
Let be a function defined on the real line
such that
for every . Prove
for all
, i.e.
is constant.
Solution:
Take any . Next, we obtain for all
.
So, for ,
.
Then, take the limit as approaches
, we get
Hence, the derivative is zero 0 everywhere. Therefore,
must be a constant function.
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