Given the condition \( a > 0 \), let's reevaluate the limit to ensure correctness with respect to the original problem.

The expression given is:

\[
\lim_{a \to 0^+} \left( \frac{2}{a} + \frac{1}{\sqrt{a}} \right) \left( 1 - \sqrt{a + 1} \right)
\]

### Step 1: Analyze the components
- \( \frac{2}{a} \) becomes large as \( a \) approaches 0 from the positive side.
- \( \frac{1}{\sqrt{a}} \) also becomes large as \( a \) approaches 0.
- \( 1 - \sqrt{a + 1} \) becomes close to \( -\frac{a}{2} \) for small values of \( a \).

### Step 2: Simplify using the approximation
For small \( a > 0 \), the square root term can be approximated by:
\[
\sqrt{a + 1} \approx 1 + \frac{a}{2}
\]
So,
\[
1 - \sqrt{a + 1} \approx 1 - \left(1 + \frac{a}{2}\right) = -\frac{a}{2}
\]

### Step 3: Substitute and simplify
Substituting this back into the original expression:

\[
\lim_{a \to 0^+} \left( \frac{2}{a} + \frac{1}{\sqrt{a}} \right) \left( -\frac{a}{2} \right)
\]

Expanding this:

\[
\lim_{a \to 0^+} \left( -\frac{2}{a} \cdot \frac{a}{2} - \frac{1}{\sqrt{a}} \cdot \frac{a}{2} \right)
\]

### Step 4: Simplify each term
1. The first term:
   \[
   -\frac{2}{a} \cdot \frac{a}{2} = -1
   \]
2. The second term:
   \[
   -\frac{1}{\sqrt{a}} \cdot \frac{a}{2} = -\frac{\sqrt{a}}{2}
   \]

As \( a \) approaches 0 from the positive side, \( \sqrt{a} \) approaches 0, so the second term goes to 0.

### Step 5: Combine the terms
Thus, the limit is:
\[
\lim_{a \to 0^+} \left( -1 - 0 \right) = -1
\]

### Final Answer
So, the correct limit, considering \( a > 0 \) and as \( a \) approaches 0 from the positive side, is still \( \boxed{-1} \).

Would you like more details or have any questions about this problem?

Here are some related questions you might find interesting:
1. What is the importance of the condition \( a > 0 \) in evaluating this limit?
2. How does the limit behavior change for different values of \( a \)?
3. What is the geometric interpretation of the function \( \sqrt{a + 1} \) near \( a = 0 \)?
4. How can Taylor series be used to approximate square roots for small values of \( a \)?
5. What other methods can be used to evaluate limits that result in indeterminate forms?

**Tip:** Always pay close attention to the conditions provided in limit problems, such as whether \( a \) approaches from the positive or negative side, as these can significantly influence the result.

Learn how to evaluate the limit lim(a -> 0+) ((2/a) + (1/sqrt(a))) (1 - sqrt(a + 1)) with a detailed step-by-step solution. This problem involves limits, approximations, and asymptotic analysis, focusing on small values of a. Suitable for advanced undergraduate mathematics.

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