Final answer:
The motile spirochete that can survive in vivo is Borrelia burgdorferi, the causative agent of Lyme disease. B. burgdorferi is capable of moving using axial filaments and is visualized using darkfield microscopy due to its thin and spiral shape.
Step-by-step explanation:
The motile spirochete that can survive in vivo is Borrelia burgdorferi. This spirochete is known for causing Lyme disease, which is transmitted by ticks and may result in symptoms such as a "bull's eye" rash, fever, fatigue, and possibly debilitating arthritis. In contrast to some other spirochetes, B. burgdorferi is notably capable of surviving and causing disease within a host organism, which is what in vivo refers to.
Spirochetes like B. burgdorferi use axial filaments for propulsion. These are effectively flagella that run the length of the spirochete, between the inner and outer membranes, allowing them to move. Darkfield microscopy is often used to visualize spirochetes because they are thin and spiral-shaped, which makes them difficult to see under standard light microscopy.