# Limit, derivative, integral, and Taylor check

> ML preparation item.

- Stable ID: `original-calc-one-variable`
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Expected time: 8 minutes
- Skills: limits-continuity, single-variable-calculus, taylor-approximation
- Item JSON: https://mlprep.iwase.dev/data/items/original-calc-one-variable.json

## Problem

Evaluate $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}$. Then, for $f(x) = x^3 - 3x^2 + 2$, compute $f'(x)$, $\displaystyle \int_0^2 f(x)\,dx$, and the second-order Taylor polynomial around $x=1$.


## Answer policy

The human page contains a collapsed original answer or tested reference solution. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `original-calc-one-variable`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.