Final answer:
A maneuver task during offensive operations where troops move around the side to attack is called a flanking maneuver. This tactic was effectively used by Grant in the capture of Vicksburg, and it plays on the element of surprise and speed against less defended positions.
Step-by-step explanation:
The maneuver tasks during offensive operations that involve moving around the side of an army, rather than attacking directly from the front, is known as a flanking maneuver. This tactic is aimed to attack the enemy from the side, where they are less protected.
The classic use of a flanking maneuver can be seen in Grant's capture of Vicksburg. The effectiveness of such maneuvers depends on the element of surprise, speed, and the ability to hold the enemy in position while a flanking force is positioned. There are other tactics like deviation, where troops take a circuitous route to surprise an enemy and the use of a siege when the enemy is entrenched.