Find the limit, if it exists: 

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Find the limit, if it exists:

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Find the limit, if it exists

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By tracing the function from left and right into the x value and looking to see what you expect to see at y. It provides a visual way to see if a limit exisits or not.

(discuss with group if your answer is close)

Create the graph of 

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 Estimate the limit as x→-3

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DNE

Create the graph of

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Estimate the limit as x→-1

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-1

Create the graph of 2x²+4x

Estimate the limit as x→-2

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0

Use the table to estimate the value of

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Use the table to estimate the value of

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Find the limit as x approaches 1 form the left and the right

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Find the limit as x approaches -2 from the left and the right: 

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A person is walking, at one point he falls, and then continues walking. What is the point at which he falls?

Animation: http://calcgame.weebly.com/

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Horizontal Asymptote

x = 4

Vertical Asymptote

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Animation: http://calcgame.weebly.com/animation-2.html

9

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x = 2/3 and x = 7

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y = 0

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greater

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y = ±1

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Vertical Asymptote

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y = 3

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y = 1

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Asymptote

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Continuous

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Decreasing

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1/2

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Animation: http://calcgame.weebly.com/animation-3.html

40

   f(c) is defined

lim_x>c  f(x) exists

lim_x>c  f(x) = f(c)

      What is one type of function that is continuous at every point in its domain?

    Polynomial Functions

Rational Functions

Radical Functions

             What is the lim_x>1   x² + 1.  Find the relationship between epsilon and delta.

  lim_x>1   x² + 1 = 2 

δ = ε

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Continuous: http://calcgame.weebly.com/animation-4b.html

Not Continuous: http://calcgame.weebly.com/animation-4a.html

  Removable discontinuity

      Hole at x=1

lim_x>0   2x-4 = -2 

Continuous

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    lim_x>π   tan x = 0

  Non-removable Discontinuity

     Graph  f(x) = x² + 4x +3. Find the slope of the tangent line at the point (3, 24).

m = 2x + 4  m =  10

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Find the slope of the tangent line

to f(x) = x³ – 5x + 2 at the point (2, 0).

  m = 3x² – 5  m = 7

      Graph  f(x) = x² -4.

Find the slope of the tangent line at (4, 12).

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m = 2x   m = 8

1.       What is the definition of the slope of the tangent line to f(x) at a point a?

           The instantaneous velocity of the original  function at point a