Lesson Worksheet: Limits from Tables and Graphs Mathematics • 12th Grade

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In this worksheet, we will practice evaluating the limit of a function using tables and graphs.

Q1:

If graph shown represents the function 𝑓(𝑥)=𝑥−3, determine lim→𝑓(𝑥).

Q2:

Determine the limit as 𝑥→2 of the function represented by the graph.

Q3:

Estimate lim→𝑓(𝑥) from the given table.

𝑥−2.1−2.01−2.001⟶−2⟵−1.999−1.99−1.9
𝑓(𝑥) 36.9 36.09 36.009 ⟶⋯⟵ 35.991 35.91 35.1

Q4:

Estimate lim→𝑓(𝑥) numerically, given that 𝑓(𝑥)=𝑥−25𝑥−5.

𝑥 4.9 4.99 4.999 ⟶ 5 ⟵ 5.001 5.01 5.1
𝑓(𝑥) 9.8 9.98 9.998 ⟶⋯⟵ 10.002 10.02 10.2

Q5:

Determine lim→𝑓(𝑥) if it exists.

Q6:

Determine the limit of the function as 𝑥→2.

  • A2
  • BThe limit does not exist.
  • C3
  • D0

Q7:

Using the graph shown, determine lim→𝑓(𝑥).

Q8:

Determine lim→𝑓(𝑥), if it exists.

  • A1
  • BThe limit does not exist.
  • C5

Q9:

Determine lim→𝑓(𝑥), if it exists.

Q10:

Determine lim→𝑓(𝑥).

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