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Mathematics · Grade 11

Limits and Continuity

Learners make 'approaching' precise. They estimate limits from tables and graphs, compare one-sided limits, evaluate limits with limit laws, factoring and rationalizing, analyze limits involving infinity, test continuity with three conditions, classify discontinuities, and use the Intermediate Value Theorem. An optional honors lesson introduces the squeeze theorem and the limit of sin x / x.

  • 5 lessons
  • About 150 minutes
  • Limits and continuity check: 12 questions
  • Ways to answer: choose an answer, match pairs, type a number, put in order, sort into groups and true or false
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What learners will discover

  • Estimate limits from tables and graphs, including one-sided limits, and decide when a two-sided limit exists.
  • Evaluate limits algebraically using limit laws, factoring and rationalizing.
  • Analyze infinite limits and limits at infinity and connect them to vertical and horizontal asymptotes.
  • Determine continuity with the three-part definition, classify discontinuities and apply the Intermediate Value Theorem.

Lessons

  1. Limits from tables and graphs 5 steps3 practiceabout 30 min
  2. Evaluating limits with algebra 5 steps3 practiceabout 34 min
  3. Limits involving infinity 5 steps3 practiceabout 30 min
  4. Continuity and the Intermediate Value Theorem 5 steps3 practiceabout 34 min
  5. Going further (honors): the squeeze theorem 4 steps2 practiceabout 22 min
  6. Limits and continuity check 12 questions at the end

Keep exploring

More 11th grade math

Guide for grown-ups