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Outcomes & Indicators
Logical Thinking, Number Sense, Spatial Sense, Mathematics as a Human Endeavour

Outcome: C30.3

Demonstrate understanding of limits and continuity. [C, CN, ME, PS, R, T, V]

  1. Develop and explain the meaning of a limit.

  2. Explain the difference between the limit of a function and the value of a function.

  3. Critique the statement, “If a function has a limit of L as x approaches a, then as x-values get close to a, the y-values of the function will get progressively closer to L.”

  4. Determine the value of a limit and express the value using limit notation when given:

    • a graph
    • an algebraic expression.
  5. Analyze the graph of a function to determine if it is continuous.

  6. Analyze the equation of a function to determine if it continuous.

  7. Develop, explain, and apply strategies for determining if a function is continuous at a given point.

  8. Develop, explain, and apply strategies for determining the type of discontinuity (removable, jump, or infinite) when given:

    • a graph
    • an algebraic expression.
  9. Develop, explain, and apply strategies (e.g., direct substitution, factoring, simplifying, rationalizing) to determine limits, at real numbers and infinity, of functions including absolute value, root, and piecewise.

  10. Identify the conditions under which a limit does not exist.

 
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