Problem Analysis #common_02

Motif 3 · Run 1

Python ● execution succeeded

Correct

8.44s

3,066 toks

Infron · Motif 3 · 46문항 × 3회 · Python TAR. 131,072 output tokens · 기본 1,800초 · 6+1 turns. ACC는 전체 138회, Pass@1은 각 문항의 첫 유효 시도, Pass@3는 3회 내 정답으로 계산합니다.

Problem Statement

함수 $f(x)=3x^3+4x+1$ 에 대하여 $\lim_{h\to0}\frac{f(1+h)-f(1)}h$ 의 값은?

① $7$ ② $9$ ③ $11$ ④ $13$ ⑤ $15$

최종 답은 선택지 번호 1~5 중 하나를 $\boxed{}$ 안에 쓰세요.

Ground Truth

Recorded model response / solution

Reasoning Process

Recorded Python call:

import sympy as sp
x, h = sp.symbols('x h')
f = 3*x**3 + 4*x + 1
limit_expr = (f.subs(x, 1+h) - f.subs(x, 1)) / h
sp.limit(limit_expr, h, 0)

Tool Output

Execution succeeded

Reasoning Process

Recorded Python call:

import sympy as sp
x, h = sp.symbols('x h')
f = 3*x**3 + 4*x + 1
limit_expr = (f.subs(x, 1+h) - f.subs(x, 1)) / h
result = sp.limit(limit_expr, h, 0)
print(result)

Tool Output

Execution succeeded 13

Reasoning Process

The expression $\lim_{h\to0}\frac{f(1+h)-f(1)}{h}$ is the definition of the derivative $f'(1)$ .

Given $f(x) = 3x^3 + 4x + 1$ , the derivative is:

f'(x) = 9x^2 + 4

Evaluating at $x = 1$ :

f'(1) = 9(1)^2 + 4 = 9 + 4 = 13

The Python computation confirms the limit equals $13$ .

$\boxed{4}$

Final Model Output

Comparative Analysis (Pcommon_02) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

Motif 3

15.8

MiMo V2.6 Pro

14.0

Solar Pro 4

12.8

Union Alpha

12.2

Grok 4.7

7.7

Muse Spark 1.3

7.2

DeepSeek V4.1 Flash

4.6

Solar Mini 4 Preview

3.1

Avg Token Usage

Grok 4.7

4,555

Union Alpha

4,444

Muse Spark 1.3

3,261

Motif 3

3,027

Solar Mini 4 Preview

2,981

Solar Pro 4

2,832

DeepSeek V4.1 Flash

2,407

MiMo V2.6 Pro

2,169