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Warm Up

Warm Up . Packet pg. 2 & 3. Problems for HW Credit. pg. 65 3: Morgan; Gil 39: Victoria; Rebecca 40: Megan; Drayton 44: Savona; Carlos 47: Decoya; Julie 48: Brenden; Brian 80: MacKenzie; LeKurt. Grab a large whiteboard and show us what you did…

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Warm Up

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  1. Warm Up Packet pg. 2 & 3

  2. Problems for HW Credit pg. 65 3: Morgan; Gil 39: Victoria; Rebecca 40: Megan; Drayton 44: Savona; Carlos 47: Decoya; Julie 48: Brenden; Brian 80: MacKenzie; LeKurt Grab a large whiteboard and show us what you did… It doesn’t have to be right but you have to show effort

  3. Homework: pg. 65 (1 – 4, 37 – 48, 79-82)Packet pg. 1 • Pg. 65 • a. 0; b. 6 • a. 2.4; b. 4 • a. 0; b. √3/6 • a. 0; b. -5 • 37. a. 15 • b. 5 • c. 6 • d. 2/3 • 38. a. 6 • b. 2 • c. ¾ • d. 3 • 39. a. 64 • b. 2 • c. 12 • d. 8 • 40. a. 3 • b. 1.5 • c. 729 • d. 9 • 41. a. 1 • b. 3 • 42. a. 1 • b. -3 • 43. a. 2 • b. 0 • 44. a. DNE • b. -1 • 45. -2 • 46. -5 • 47. 12 • 48. 3 • 79. 3 • 80. 2 • 81. 0 • 82. 0 Packet pg. 1 1. T: a, b, d, e, f 2. F: b, c 3. C 4. B 5. D 6. A

  4. AP Calculus AB Evaluating Limits Algebraically

  5. DISCLAIMER: • The limit of f(x) as x approaches c DOES NOT depend on the value of f(c). • However, sometimes you get a gift and it’s a simple plug & chug problem when: For these problems, simply sub in x = c. i.e. DIRECT SUBSTITUTION

  6. How to tell when you can use DIRECT SUBSTITUTION: • The function needs to be “well-behaved” (continuous) at c. • Which means (informally): • It is usually easy to try this in your head. • No holes • No jumps • No asymptotes • You never have to pick up your pencil.

  7. Thm: • If 2 functions agree at all but one point, then So, what’s the big deal?...Helps us fill in the holes!!

  8. Trick 1: Factoring f(-4) D.N.E., however

  9. Practice:

  10. Note: When direct substitution produces 0/0, the expression is called Indeterminate Form… Trick 2: Rationalize the square root… Remember Conjugates?!?...

  11. You try:

  12. Trick 3: Multiply by 1 in a “convenient form” (The common denominator)

  13. One last way to find a limit… Squeeze Thm (aka Sandwich Thm): If and then *Good for finding limits involving trig functions

  14. Big Picture

  15. Example 2:

  16. Thm: KNOW THESE!! (hint!)

  17. Examples: 1. 2.

  18. Strategies for Finding Limits: 1. Go for the easy path 1st!! Try direct substitution 2. Try to change the function into one that can be solved by direct substitution (see previous slide) 3. Apply theorem to conclude that 4. Remember you can always graph to check! …But sometimes there is NO LIMIT. Bwauh-haa-haa!!!

  19. Limit Dominos

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