$1.$ Consider the B$+$ tree index. Every node can contain m entries, where $2$ m $4.$ The root node is an exception: it allows $1$ m $4.$ A$.$ Show the B$+$ tree that would result from inserting data entries with key $30,33,$ and $41$ into the tree. $($Insert each entry one at a time and show all work$)$B$.$ Given the output of $($A$),$ show the B$+$ tree that would result from deleting the data entry with key $3.$ C$.$ Given the output of $($B$),$ show the B$+$ tree that would result from deleting the data entry with key $4.$ D$.$ Given the output of $($C$),$ show the B$+$ tree that would result from deleting the data entry with key $15.$Consider the B$+$ tree index.

Every node can contain m entries, where $2m4.$

The root node is an exception: it allows $1m4.$

B$+$ tree

A$.$ Show the B$+$ tree that would result from inserting data entries with key $30,33,$ and $41$ into the tree. $($Insert each entry one at a time and show all work$)$

B$.$ Given the output of $(A),$ show the $B+$ tree that would result from deleting the data entry with key $3.$

C$.$ Given the output of $(B),$ show the $B+$ tree that would result from deleting the data entry with key $4.$

D$.$ Given the output of $(C),$ show the $B+$ tree that would result from deleting the data entry with key $15.$