2-5-31
X
00:00
/
00:00
CC
For this problem, we're going to stick in seven Pi eighteenths,
so the limit as X approaches 7 Pi eighteenths of cosine 9X
minus cosine of 9X.
So when we stick in seven Pi eighteenths, we're going to get
cosine of 9 * 7 Pi eighteenths minus cosine of 9 * 7 Pi
eighteenths.
Well, 9 * 7 Pi eighteenths is going to give me 7 Pi halves,
because remember that nine is understood over 19 and 18
reduced to 1/2 minus cosine of.
Once again, this one's going to reduce to seven Pi halves.
What is cosine of seven Pi halves?
Cosine of any K π half is 0, so we're going to have cosine 7 Pi
halves -0 seven Pi halves -0 is going to be cosine of seven Pi
halves again, and cosine of any K Pi halves is going to be 0.
Actually I should say any K Pi halves where K is an odd integer
because 2π halves would be a π and cosine of π is not zero.
So Pi halves three Pi halves 5 Pi halves -1 half Pi -3 halves
Pi, etcetera.
So that's our final answer.
There was a Part 2 of this problem and the Part 2 wants to
know is this continuous?
And so we want to know if I put in seven Pi eighteens without
the limit portion, is that location defined?
And our answer is yes, because we just did a straight
substitution.
We didn't have to use a conjugate or a theorem or
anything else to reduce it down.
So yes, it is continuous at this location.