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Limits

Limits. Limits By: Table of Values Graph Piece-Wise Functions. Problem of the Day. Express the following sequences recursively: {-3, 1, 5, 9, ...} {4, 12, 36, 108, ...} Determine the sum of the following series. Label as either convergent or divergent at ∞ and give a reason.

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Limits

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  1. Limits Limits By: Table of Values Graph Piece-Wise Functions

  2. Problem of the Day • Express the following sequences recursively: • {-3, 1, 5, 9, ...} • {4, 12, 36, 108, ...} • Determine the sum of the following series. Label as either convergent or divergent at ∞ and give a reason.

  3. Journal Entry #1 • First, create a new section in your journal for Pre-Calculus 12 (it’s great to be organized). • Then, complete the following problem: • Using mathematical induction, prove the following statement: • is divisible by 6.

  4. What is a Limit? • Find a partner and discuss the following questions: • How would you define the word limit? • What are some limits that exist in our daily lives? • Where might limits occur in mathematics?

  5. Mathematical Limits • Limit– The value a function or sequence approaches (f(x)-value, y-value or tn-value) as the input or index (x-value or n-value) approaches some number • c is the index. It is the value that the function is approaching. • f(x) is the function being analysed.

  6. Consider • Rewrite the function in transformational form (T.F.) • Determine the function’s mapping rule, original coordinates and transformed coordinates. • Graph the function.

  7. Left Hand Limit = Right Hand Limit (LHL = RHL) • What value does the function approach as x approaches 4 from the left hand side? (x->4-) • What value does the function approach as x approaches 4 from the right hand side? (x->4+) • Does the LHL=RHL? • Therefore, the limit of the function as x approaches 4 is -1.

  8. Left Hand LimitRight Hand Limit Left Hand Limit = Right Hand Limit LHL = RHL

  9. Limits by Tables of Value • Let’s examine the table of values for as x->4 The values of y converge at -1 as x approaches 4 from the left and the right hand side. The limit of y as x approaches 4 is -1. -1

  10. You Try... • Complete Sheet 7.1

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