To evaluate the limit lim h → 0 of √(4h² + h), we start by substituting h with 0 in the expression.
When we do this, we have:
√(4(0)² + (0)) = √(0) = 0
So, the limit is:
0
This limit tells us about the behavior of the function as h approaches 0. Essentially, as h gets very close to 0, the entire expression inside the square root also approaches 0, leading to the final result of the limit being 0.