For each n ∈ n, let fn(x) = (cos x)n. each fn is a continuous function. nevertheless, show (a) lim fn(x) = 0 unless x is a multiple of π, (b) lim fn(x) = 1 if x is an even multiple of π, (c) lim fn(x) does not exist if x is an odd multiple of π.

See explanation below.

Step-by-step 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.

d

step-by-step explanation:

answer: 819.89 miles across america

step-by-step explanation: