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Warm Up Packet pg. 2 & 3

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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

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Homework: pg. 65 (1 – 4, 37 – 48, 79-82) Packet pg. 1 Packet pg. 1 1. T: a, b, d, e, f 2. F: b, c 3. C 4. B 5. D 6. A Pg. 65 1.a. 0; b. 6 2.a. 2.4; b. 4 3.a. 0; b. √3/6 4.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

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AP Calculus AB Evaluating Limits Algebraically

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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

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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.

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

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

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Practice:

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

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You try:

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

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

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Big Picture

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Example 2:

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Thm: KNOW THESE!! (hint!)

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Examples: 1. 2.

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Strategies for Finding Limits: 1. Go for the easy path 1 st !! 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!!!

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Limit Dominos

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Limits Analytically. Find the limit of Steps to Solve for Limits 1) Substitute the value in 2) Factor and Cancel (maybe rationalize) 3) The answer is.

Limits Analytically. Find the limit of Steps to Solve for Limits 1) Substitute the value in 2) Factor and Cancel (maybe rationalize) 3) The answer is.

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