Final answer:
In a case of deep vein thrombosis, the nurse would most likely observe swelling in the lower extremity as a key symptom. The other options are less indicative of DVT and more commonly associated with other conditions.
Step-by-step explanation:
The nurse assessing a client with a deep vein thrombosis (DVT) would anticipate finding certain specific signs and symptoms associated with the condition. Among the options provided, the symptom most definitely associated with DVT is C) Swelling of lower extremity. This is due to the blockage of blood flow in the veins which can lead to fluid accumulation and swelling. The other symptoms listed, such as rapid respirations, diaphoresis, and a positive Babinski's sign, are not directly indicative of deep vein thrombosis. Instead, they are more commonly associated with other medical conditions.