Answer & Explanation
Multiply both sides by x and take the square root:
Therefore, , and solving we have
It is important to show that the limit exists. Let define the sequence
Since and , we have
1. if , then ; that is, is increasing and bounded above by n.
2. if , then ; that is, is decreasing and bounded below by n.
In either case, is convergent. Using the continuity of multiplication by a constant and the continuity of square root, we get
Squaring and dividing by , we get that