Compressed Set of the Entire Limits & Continuity Curriculum

Question One: Test Your Understanding of Limits

Consider the piecewise function f(x) defined above, whose behavior near x=2 is represented in the table and graph. 

Part A: Write the limit notation for the value that f(x) approaches as x approaches 2 from the left, and state its value based on the table and graph. 

Part B: Write the limit notation for the value that f(x) approaches as x approaches 2 from the right, and state its value based on the table and graph. 

Part C: Does the limit of f(x) as x approaches 2 exist? Express your conclusion using proper limit notation and explain why or why not. 

Question Two: Mastering Direct Substitution for Limits

Evaluate the following limit: 

Select answer:
A) -34/7
B) 34/7
C) -4/7
D) DNE

Question Three: Factorization after Direct Substitution fails

Evaluate the following limit:

Select answe:
A) -8/11
B) 0
C) 8/11
D) DNE

Question Four: Rationalization after Direct Substitution fails

Evaluate the following limit: 

Select answer:
A) 0
B) 6
C) DNE
D) 1/6

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