Use the previous exercise (Section 10.4, Exercise #34) to establish each of the following limits.

- .
- .
- .
- .
- .
- .

- Let , then from Exercise #34 we know
where

Thus,

(since and then use the squeeze theorem). So,

- Let
So,

Thus,

- Let
Thus,

Therefore,

- Let
Thus,

So,

- Let
Thus,

Therefore,

- Let
Thus,

Therefore,

First, most of these functions are not increasing but this can be fixed by multiplying by -1, however there is big problem with (e) since it’s not monotonic… but I managed to prove it by substituting 2n instead of n and then breaking the sum into two parts one is usual since sin(xpi/2) is increasing on [0,1] and the other part you just change the indexing and you get a cosine which can be dealt with as usual.

part (f) is similar