Question

Evaluate the limit if it exists: lim h → 0 (√(4h) - 2)/h

Answer 1

To evaluate the given limit, (√(4h) - 2)/h as h approaches 0, we simplify the expression and then take the limit. The final answer is 2.

Step-by-step explanation:

To evaluate the limit lim h → 0 (√(4h) - 2)/h, we can simplify the expression first. Let's start by simplifying the numerator: √(4h) - 2. We can factor out a 2 from the square root to get 2√h - 2. Now we can combine like terms in the numerator: 2√h - 2.

Next, we divide both the numerator and denominator by h: (2√h - 2)/h. Finally, we take the limit as h approaches 0. As h approaches 0, the term 2/h becomes ∞ and the term 2h in the square root becomes 0. Therefore, the limit evaluates to 2.