Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u12-l05', 'number': 5, 'title': 'Continuity, Discontinuity & End Behavior', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Find the average rate of change of x² from 2 to 5.
2. {'id': 'u12-l05', 'number': 5, 'title': 'Continuity, Discontinuity & End Behavior', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Simplify [(x+h)²−x²]/h.
3. {'id': 'u12-l05', 'number': 5, 'title': 'Continuity, Discontinuity & End Behavior', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→3}(2x+1).
4. {'id': 'u12-l05', 'number': 5, 'title': 'Continuity, Discontinuity & End Behavior', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→2}(x²−4)/(x−2).
5. {'id': 'u12-l05', 'number': 5, 'title': 'Continuity, Discontinuity & End Behavior', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Can a two-sided limit exist if one-sided limits differ?
6. {'id': 'u12-l05', 'number': 5, 'title': 'Continuity, Discontinuity & End Behavior', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Name the discontinuity in (x²−1)/(x−1) at x=1.
7. {'id': 'u12-l06', 'number': 6, 'title': 'Instantaneous Change and Accumulation Preview', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Find the average rate of change of x² from 2 to 5.
8. {'id': 'u12-l06', 'number': 6, 'title': 'Instantaneous Change and Accumulation Preview', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Simplify [(x+h)²−x²]/h.
9. {'id': 'u12-l06', 'number': 6, 'title': 'Instantaneous Change and Accumulation Preview', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→3}(2x+1).
10. {'id': 'u12-l06', 'number': 6, 'title': 'Instantaneous Change and Accumulation Preview', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Evaluate lim_{x→2}(x²−4)/(x−2).
11. {'id': 'u12-l06', 'number': 6, 'title': 'Instantaneous Change and Accumulation Preview', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Can a two-sided limit exist if one-sided limits differ?
12. {'id': 'u12-l06', 'number': 6, 'title': 'Instantaneous Change and Accumulation Preview', 'family': 'limits', 'week': 34, 'unit': 12, 'unit_title': 'Limits & Calculus Readiness', 'essential': 'How do local behavior, average and instantaneous change, limits, continuity, and accumulation prepare learners for calculus?', 'project': 'Change, Limit & Accumulation Readiness Portfolio'}
Name the discontinuity in (x²−1)/(x−1) at x=1.