The limit lim(x→0) √(3/x) does not exist. As x approaches 0, the value of √(3/x) approaches positive infinity, not a specific number.
As x approaches 0 from the positive side (x > 0), the value of √(3/x) gets increasingly larger because 1/x gets increasingly larger.
This is because √(a/b) = √a / √b, and since √a is always positive, the behavior is dominated by 1/x.
As x approaches 0 from the negative side (x < 0), the value of √(3/x) becomes imaginary because 3/x becomes negative.
Since the limit requires the function to approach a single real value, the limit does not exist.
Therefore, we can conclude that lim(x→0) √(3/x) does not exist.