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Review: 1. What is a limit? 2. Is the slope a rate? Why or why not?

Review: 1. What is a limit? 2. Is the slope a rate? Why or why not? 3. Can a rate be infinitesimal?. Vocabulary: Limit: The value a function approaches as the x value gets closer and closer to it's target.

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Review: 1. What is a limit? 2. Is the slope a rate? Why or why not?

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  1. Review: 1. What is a limit? 2. Is the slope a rate? Why or why not? 3. Can a rate be infinitesimal?

  2. Vocabulary: Limit: The value a function approaches as the x value gets closer and closer to it's target. Left/Right hand limits: The limits as we approach from the left or right hand side. If the left and right hand limits are equal, the limit exists. Left hand limit: Right hand limit:

  3. Properties of Limits If L, M, c, and k are real numbers and and , then

  4. Functions and Limits For 1 & 2, just plug in the value and solve. 3 is a definition.

  5. Sandwich Theorem If g(x) ≤ f(x) ≤ h(x) for all x≠c for some interval about c and h(x) then, f(x) g(x)

  6. Ex 1: Find the limit.

  7. Ex 2: Verify that the limit does not exist.

  8. Ex 3: Determine the limit graphically and algebraically a) lim n2 - 3n + 2 b) lim x + sin x x 2 n2 - 4 x 0 x

  9. Ex 4: Find the limit a) lim int x b) lim ||x|| x 1+ x 1- c) lim x d) lim x x 0+ |x| x 0- |x|

  10. Ex 4: Use the graph to find the limits a) lim f(x) b) lim f(x) c) lim f(x) x 1- x 1+ x 1 d) lim f(x) e) lim f(x) f) lim f(x) x 2+ x -1 x -2+

  11. Assignment: p 66 # 3-36(x3), 38, 47, 50, 51, 54, 55, 61, 64

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