Calc 1.3a
- 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
- 3. Properties of Limits p. 59 Ex. 1 p. 59 a. b. c.
- 4. p. 59
- 5. Ex 2, p. 60 Limit of a Polynomial
- 6. Ex 3 p. 60 The Limit of a Rational Function
- 7. Polynomial functions , rational functions , and radical functions make up the three basic types of algebraic functions.
- 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,
- 9. On to some transcendental functions (functions that are not algebraic in nature)
- 10. Ex 5 p. 61 Limits of Trigonometric Functions
- 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
- 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.
- 13. 1.3 p.67/ 1-49 every other odd (EOO)