1. Finding Limits Graphically and Numerically
Rizzi – Calc BC

2. Simple example
𝒇 𝒙 = 𝒙 𝟒 −𝟏 𝒙−𝟏 Find 𝒇 𝟐 = Find 𝒇 −𝟏 = Find 𝒇 𝟏 =

3. lim 𝒙→𝟏 𝒙 𝟒 −𝟏 𝒙−𝟏 = Limit Notation
We can’t actually evaluate 𝒇 𝟏 for 𝒇 𝒙 = 𝒙 𝟒 −𝟏 𝒙−𝟏
Instead, we can use limit notation to describe where the function goes
lim 𝒙→𝟏 𝒙 𝟒 −𝟏 𝒙−𝟏 =

4. Use a numerical approach to find: lim 𝒙→𝟎 𝒔𝒊𝒏(𝟏𝟎𝒙) 𝒙
Harder examples
Use a numerical approach to find: lim 𝒙→𝟎 𝒔𝒊𝒏(𝟏𝟎𝒙) 𝒙 x y

5. lim 𝒙→𝟎 (𝟏+𝒙) 𝟏/𝒙 Harder examples Use a numerical approach to find: xy

6. Limits that Fail to Exist
With your partner, investigate one of the two of these numerically:
lim 𝒙→𝟎 |𝒙| 𝒙
lim 𝒙→𝟎 𝒔𝒊𝒏(𝟏/𝒙)

7. lim 𝒙→−𝟏 𝒇(𝒙) = 𝒇(−𝟏)= lim 𝒙→−𝟒 𝒇(𝒙) = 𝒇(−𝟒)=
Graphical Limits
lim 𝒙→−𝟏 𝒇(𝒙) = 𝒇(−𝟏)= lim 𝒙→−𝟒 𝒇(𝒙) = 𝒇(−𝟒)=