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1.5 Properties of Limits

1.5 Properties of Limits. Assigned work: pg 45 #1, 4ac,7def,8def,9ad,10,15,17 . 1.5 Properties of Limits. 1.5 Properties of Limits. Other handy limit information:. 1.5 Properties of Limits. More handy limit information: When you evaluate limits if when you sub in the x value you get

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1.5 Properties of Limits

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  1. 1.5 Properties of Limits Assigned work: pg 45 #1, 4ac,7def,8def,9ad,10,15,17 S. Evans

  2. 1.5 Properties of Limits S. Evans

  3. 1.5 Properties of Limits Other handy limit information: S. Evans

  4. 1.5 Properties of Limits • More handy limit information: • When you evaluate limits if when you sub in the x value you get • a #, then it is a point and function exists there • , then function is a hole at that point. • , then function has a vertical asymptote at that point S. Evans

  5. 1.5 Properties of Limits Recall: Limit exists IFF LHL=RHL and it can exist even if the function does not exist at that point. Today we’ll examine “Indeterminant Limits where the result is when you sub in. How to Evaluate a Limit: Check if LS and RS exist. Try substituting the x-value in. For indeterminant limits: a) simplify b) factor c) rationalize OR d) separate into piecewise. (examine LS & RS separately) S. Evans

  6. 1.5 Properties of Limits Ex 1: Evaluate: a) Watch Form… State restrictions Use brackets Know when to drop limit sign Know how to show graphically (i.e. line with hole at (3,6) S. Evans

  7. 1.5 Properties of Limits Ex 1: Evaluate: b) Be careful!! Square root signs! Check if LHL & RHL exist and are = S. Evans

  8. 1.5 Properties of Limits Ex 1: Evaluate: c) Check that both sides of limit exist – they do in this example Rationalize Watch how to expand/simplify efficiently (i.e. numerator but leave denominator) Solution on next slide S. Evans

  9. 1.5 Properties of Limits Solution: c) S. Evans

  10. 1.5 Properties of Limits Ex 1: Evaluate: d) Check that both sides of limit exist – they do in this example Simplify Multiply num & den by common denomof individual terms Common factor out -1 in denom so that you can cancel a term (where hole is) S. Evans

  11. 1.5 Properties of Limits Solution: d) S. Evans

  12. 1.5 Properties of Limits Ex 1: Evaluate: e) f) Note: indeterminant absolute value functions …examine LS and RS by creating a piecewise function. See solution next slide S. Evans

  13. 1.5 Properties of Limits Solution: f) Piecewise function created. S. Evans

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