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Finding Limits Graphically.notebook
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finding limits numerically
and graphically
Ch.12 Lesson 1
Finding Limits Graphically.notebook
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Target
Agenda
Purpose
Evaluation
TSWBAT: Find the limit of a function given its graph or a table.
Warm-Up
Lesson
BAT: Get ready for calculus. Extend knowledge functions, make connections, apply knowledge to new situations
3-2-1
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Warm-Up:
1.
2.
3.
What did you do well on?
What specifically do you need to look back on and learn?
How excited are you to be on the last unit of the semester?
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Reaching your limit
What happens to you as your sibling keeps bothering you more and more?
What happens to your willingness to do a chore as your parents keep telling you to do it?
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As x approaches a, f(x) approaches L
Remember...
as x ⇒∞, y ⇒a
as x ⇒a, y ⇒∞
What if we aren't specifically looking at asymptotes?
Can the function pass y=3 as x keeps going to the left? What might you call y=3?
as x ⇒a, y ⇒L
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Limit Notation
lim f(x) = Lx ⇒ a
The values of f(x) (the y values) get closer to the number L as x gets closer and closer to the number a from either side of a, but x≠a.
As x approaches a, f(x) approaches L
as x ⇒a, y ⇒L
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ex. What does f(x) approach to as x approaches 2
lim ( 2x2 2x + 4) =
Finding the Limit NumericallyUse your calculator
1. type in the function
2. Go to tblset and adjust Tbl = .001 and TblStart = 1.998
X Y1.9971.9981.99922.0012.0022.003
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Cool Tips
F(x) doesn't have to be defined at a, just approach it from both sides
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Finding the Limit Graphically
lim f(x) =x⇒1
lim f(x) =x⇒3
lim f(x) =x⇒2
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The limit is undefined!
when the function is...
a Piecewise function with a jump at the point a that x approaches) :
lim f(x) =
lim f(x) =
lim f(x) =
an Oscillating function : f(x) = sin (π/x)
has a Vertical Asymptote : f(x) = 1/x2
x⇒1
x⇒2
x⇒1
lim f(x) =x⇒1
lim f(x) =x⇒0
lim f(x) =x⇒2
lim f(x) =x⇒∞
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One Sided Limits
the limit of f(x) as x approaches 2 from the left
the limit of f(x) as x approaches 2 from the right
lim f(x) =x⇒2
lim f(x) =x⇒2+
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Does the limit exist? The Test
lim f(x) = L, iff lim f(x) = L = lim f(x)x⇒a x⇒a x⇒a+
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Summarizing
TIME!
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Evaluation:1.
2.
Practice! pg.889 # 126 Do 1 skip 2
lim f(x) =x⇒4
lim f(x) =x⇒2+