\text { 2. Let }\left\{a_{i}\right\}_{i=0}^{\infty} a_{n+1}=\frac{1}{2}\left(a_{n}+\frac{4}{a_{n}}\right) be the sequence starting at ao = 4, with recurrence relation (a) Prove whether the sequence is increasing, decreasing,or neither. (b) Prove whether or

not the sequence is bounded. (c) If possible, use the above to find the limit of the sequence.