# Limit, continuity, derivative, and integral

> ML Prep screening item.

- Stable ID: `math-calc-01-removable-limit`
- Collection: screening
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Difficulty: easy
- Expected time: 3 minutes
- Skills: limits, continuity, single-variable-differentiation, single-variable-integration
- Item JSON: https://mlprep.iwase.dev/item/math-calc-01-removable-limit.json

## Problem

For $x\ne1$, let $f(x)=(x^2-1)/(x-1)$. Choose $f(1)$ so that $f$ is continuous.
For that continuous extension, find $f'(1)$ and $\int_0^2 f(x)\,dx$.


## Answer policy

The human page contains a collapsed answer. 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 `math-calc-01-removable-limit`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.