Limits from a Graph

Limits from a Graph

* Limits at a point

* Left & Right Limits

* Limit Does No Exist

Limit at a Continuous Point

• Go to the X value of where the limit approaches

• Give the Y value the function approaches at the X value

Multiple Choice

$$\lim_{x\rightarrow0}$$  

• 0

• Does Not Exist

• 1

• -1

Multiple Choice

$$\lim_{x\rightarrow-1}$$  

• 0

• 1

• -1

• Does Not Exist

Left & Right Hand Limits

• Go to the X value the limit is approaching

• + : Look to the right value

• - : Look to the left value

• Note: If the function is continuous, the left and right hand limits are equal

Multiple Choice

$$\lim_{x\rightarrow-1^-}$$  

• -2

• 1

• 0

• Does Not Exist

Multiple Choice

$$\lim_{x\rightarrow-1^+}$$  

• 0

• 1

• -2

• Does Not Exist

Multiple Choice

$$\lim_{x\rightarrow0^-}$$  

• 0

• -3

• -2

• Does Not Exist

Limit Does Not Exist

• If the left and right hand limit are not equal the limit Does Not Exist

• The Limit does Exist, even if the value is not equal to the limit

Multiple Choice

$$\lim_{x\rightarrow-1}$$  

• 1

• 2

• -3

• Does Not Exist

Multiple Choice

$$\lim_{x\rightarrow1}$$  

• 1

• 0

• -1

• Does Not Exist

Multiple Choice

$$\lim_{x\rightarrow1}$$  

• 4

• 2

• 1

• Does Not Exist