Limit of \( \displaystyle \sqrt{x + 4} \) as \( x \to 5 \)
Problem 1.128 · easy
Evaluate \( \displaystyle \lim_{x \to 5} \sqrt{x + 4} \).
- \[ \lim_{x \to 5^+} \sqrt{x + 4} \]limitStart with the given limit.✓ Proved
- \[ = 3 \]limit algebra simplifySince the function is continuous at x = 5, we can evaluate by direct substitution. Perform the addition inside the square root. 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 |
| 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
Every verdict on record (4)
qwen3.6:27b-mlx: pass 2026-10-03gpt-oss:20b: pass 2026-10-03qwen3.6:27b-mlx: pass 2026-10-03gpt-oss:20b: pass 2026-10-03
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 2026-10-03 with SymPy 1.14.0.