Final answer:
The peripheral device used to control a cursor with a finger on a notebook computer is a touchpad, also called a trackpad, which is common in modern laptops.
Step-by-step explanation:
The type of peripheral device that is typically found on a notebook computer and allows the user to control the cursor with a finger is known as a touchpad or trackpad
It's a flat, tactile surface that detects pressure and movement of the user's finger to move the cursor on the screen. The touchpad is a common feature in modern laptops, replacing the need for an external mouse. Precision touchpads offer additional gestures and features, enhancing the user's control over their device.