Answer:
See explanation below.
Explanation:
For this case we have this function:

We have that this function is cotinuous and we eant to calculate the
Part a
From the results above we see that the limit only exists if x is an even multiple of
.
For the other case when x is not a multiple of
we have that:
and then we can find the limit like this:

Because the cos is a number between 0 and 1.
Part b
Assuming that x is an even multiple of
, then cos (x)=1.
If x is an even number multiple of
.
For example
we have that we can express:
And on this case

And for the limit we have that:
.
Part c
Assuming that x is an odd multiple of
, then cos (x) =-1
If x is an odd number multiple of
for example
we have that we can express:
And on this case

And since we have an alternating series we have that this limit:
not exists.