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Warmup (no calculator):

Warmup (no calculator):. 2.1a- Limits (Day 1). http://www.online.math.uh.edu/HoustonACT/. “The limit of f of x as x approaches c is L .”. The limit exists if the function approaches the same single number (L) from both sides of c. Limit notation:. Read as:.

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Warmup (no calculator):

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  1. Warmup (no calculator):

  2. 2.1a- Limits (Day 1) http://www.online.math.uh.edu/HoustonACT/

  3. “The limit of fof x as x approaches c is L.” The limit exists if the function approaches the same single number (L) from both sides of c Limit notation: Read as: read as “the limit of f(x) as x approaches 1 is 3”

  4. Reason 2 Reason 3 (sin 1/x) Reason 1

  5. 5 Ways to EVALUATE A LIMIT: #1: Graphically: (visually) Graph the function and see where it’s going #2: Numerically: (table) Make a table of values very close to the value you want to evaluate … (be sure to use numbers to the right AND to the left whenever possible) #3: Substitution: Just plug in the value where you want to evaluate the limit. If you get … DO SOMETHING ELSE!

  6. 5 Ways to EVALUATE A LIMIT (con’t): #4: Analytically (Algebraically): • -Factor the numerator and denominator and cancel any like factors. • Multiply by a factor of 1 (Includes rationalizing the numerator,denominator) • - Simplify the equation use algebraic properties and/or trigonometric identities. #5: Sandwich Theorem: Find two other functions that bound the original function AND that go to the same place at the point you are trying to evaluate the limit.

  7. The limit of a function refers to the value that the function approaches, not the actual value (if any). (1)Graphical 1 Not 0

  8. Graphical Example 4 3 3.7 ish

  9. Graphical Example 2 1.75 1 DNE

  10. [0-3(1)]=-3 [2(2)]2=16 -1 1 = -2

  11. One-sided limits approach from either the left or right side only.

  12. left hand limit right hand limit value of the function value of the two sided limit Graphical Example 2 1 1 2 3 4 At x=1: does not exist

  13. Graphical example left hand limit right hand limit value of the function 2 1 1 2 3 4 At x=2: 1

  14. GraphicalExample DNE 4 2 3

  15. 2) Numerical Example If I wanted to know f(1), you cant just plug it in. So use limits Make a table of values from both sides Around the value as we can see, it approaches 3 from both sides, so…

  16. Numerical Example =0.5

  17. Homework p. 62 (1-6, 31,32,43,44,45,46)

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