Limit of \( \displaystyle \sqrt{2 x + 4} \) as \( x \to \frac{5}{2} \)
Problem 1.238 · easy
Evaluate \( \displaystyle \lim_{x \to \frac{5}{2}} \sqrt{2 x + 4} \).
- \[ \lim_{x \to \frac{5}{2}^+} \sqrt{2 x + 4} \]limitStart with the limit expression.✓ Proved
- \[ = 3 \]limit algebra algebra simplifySince the function is continuous at x = 5/2, we can evaluate by direct substitution. Multiply 2 by 5/2. Add 5 and 4. Calculate the square root.✓ Proved
Answer \( 3 \)
✓ Nihil obstat Every line of this solution was proved by the computer algebra system SymPy. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation.
The full receipt
| Line | Status | Checked by | Detail |
|---|---|---|---|
| 1 | ✓ Proved | sympy 1.14.0 | line 1 is the problem as stated |
| 2 | ✓ Proved | sympy 1.14.0 | simplify(a - b) reduced to 0 |
| 3 | ✓ Proved | sympy 1.14.0 | simplify(a - b) reduced to 0 |
| 4 | ✓ Proved | sympy 1.14.0 | simplify(a - b) reduced to 0 |
| 5 | ✓ Proved | sympy 1.14.0 | simplify(a - b) reduced to 0 |
| answer | ✓ Proved | sympy 1.14.0 | final line against the stated answer: simplify(a - b) reduced to 0 |
| answer, a second way | ✓ Proved | sympy 1.14.0 | SymPy took the limit from both sides and got the stated value |
Reviewers
gpt-oss:20b: passqwen3.6:27b-mlx: pass — The solution correctly applies direct substitution for a continuous function and performs the arithmetic simplifications step-by-step with appropriate labels.
Every verdict on record (4)
qwen3.6:27b-mlx: pass 2026-10-05 — The solution correctly applies direct substitution for a continuous function and performs the arithmetic simplifications step-by-step with appropriate labels.gpt-oss:20b: pass 2026-10-05qwen3.6:27b-mlx: pass 2026-10-05gpt-oss:20b: pass 2026-10-05
Proved: SymPy reduced the difference between the two sides to zero. Checked independently: a separate
method, named above, confirmed it. Checked numerically: the two sides agree at every sampled point, which is evidence,
not proof. Reviewed: a model or a person read it; that is all a sentence can have. Solution by
gemma4:26b, checked 2026-10-05 with SymPy 1.14.0.