AIM: How do we find limits of a function graphically?

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Presentation transcript:

AIM: How do we find limits of a function graphically? Do Now: Find the equation of the tangent line y = x2 at x = -2 HW2.2a - p77 – 78 # 7, 8, 37, 38, 44, 45, 46, 47, 49

Find the equation of the tangent line y = x2 at x = -2

HW2.1: p66-67 #9,10,19,22,23 HOMEWORK ANSWERS?

What is a limit? As x gets closer and closer to a value, what does y get closer and closer to? The approach is more important than the actual value! What happens as: X → 2? X → 4? X → 6? X → 8? What happens as “x approaches 2” or as “x tends to 2”?

Does the limit exist at “a hole”? The limit itself exists if f(x) approaches or converges to a value regardless if f(x) exists. Let the following graph be f(x) The limit of f(x) “approaches” or “converges” to…

The limit itself exists if both one-sided limits exist and are equal. What is the limit at x = 0? “approaches 0 from the right” “approaches 0 from the left”

Infinite Limits?

Practice 1. 2. 3. 4. 5. 6. When does a limit exist???

Challenge Draw the graph of a function given the following: