Help me solve this DBWS exercise$\mathrm{.}1$ Indexing

Consider the B$+$ tree index shown in the Fiqure $1.$ Each intermediate node can hold up to five

pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doubly

linked as usual, although these links are not shown in the figure. $11$ is the root node of the tree.

Task $1\mathrm{.}1(1$ pts$)$: Name all the tree nodes that must be fetched to answer the following query:

"Get all records with search key greater than $38."$

Task $1\mathrm{.}2(3$ pt$)$: Name a search key value such that inserting it into the $($original$)$ tree would

cause an increase in the height of the tree. Explain why the height will increase.

Task $1\mathrm{.}3(5$ pts$)$: Note that subtrees A$,$ B$,$ and C are not fully specified. Nonetheless, what can

you infer about the contents and the shape of these subtrees? Consider the height, range of

search keys, and the minimum number of key values and pointers that each intermediate node

has.

Figure $1$: B$+$ tree