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# Calc 1.3a

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### Calc 1.3a

1. 2. We talked about functions that were very well-behaved – their limit of f(x) as x approaches c was actually at f(c)! In other words, just plug in x=c, and the limit pops out! These functions are continuous at c, and we’ll look more closely at the idea of continuity in 1.4
2. 3. Properties of Limits p. 59 Ex. 1 p. 59 a. b. c.
3. 4. p. 59
4. 5. Ex 2, p. 60 Limit of a Polynomial
5. 6. Ex 3 p. 60 The Limit of a Rational Function
6. 7. Polynomial functions , rational functions , and radical functions make up the three basic types of algebraic functions.
7. 8. Theorem 1.5 shows how to analyze a composite function. Ex 4 p. 61: The Limit of a Composite Function Because and With Thm 1.5,
8. 9. On to some transcendental functions (functions that are not algebraic in nature)
9. 10. Ex 5 p. 61 Limits of Trigonometric Functions
10. 11. Is there an equivalent function such that when c is plugged in, it doesn’t have an indeterminant form? (Not in form 0/0, which means from the form alone you cannot find limit) Hint: Sum of cubes, difference of cubes, this is so much fun! Ex. 6 p. 62 Find another function that is equivalent
11. 12. That last problem showed the “dividing out” technique! Ex. 7 p. 63 Hint: look for common factor! When you try to evaluate a limit that with direct substitution gives division by zero, try to rewrite the fraction so that the new denominator does not have 0 as its limit.
12. 13. 1.3 p.67/ 1-49 every other odd (EOO)