Worksheet: Limits from Tables and Graphs

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

Q1:

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

𝑥4.94.994.999⟶5⟵5.0015.015.1
𝑓(𝑥)9.89.989.998⟶⟵10.00210.0210.2

Q2:

Determine lim→9𝑒−9𝑡 by evaluating the function at the following values of 𝑡: ±0.5, ±0.1, ±0.01, ±0.001, and ±0.0001.

Q3:

Determine lim→−𝑥+10𝑥𝑥−100, if it exists, by evaluating the function at the following values of 𝑥: −9.5, −9.9, −9.95, −9.99, −9.999, −9.9999, −10.5, −10.1, −10.05, −10.01, −10.001, and −10.0001, rounding the result to the nearest six decimal places.

  • A−10
  • BThe limit does not exist.
  • C−12
  • D0

Q4:

Determine the limit as 𝑥→−1 of the function represented by the graph.

Q5:

Determine the limit as 𝑥→−3 of the function represented by the graph.

Q6:

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

Q7:

Given that the following graph represents the function 𝑓(𝑥)=𝑥−4𝑥+2, determine lim→𝑓(𝑥).

Q8:

Determine the limit of the function as 𝑥→3.

Q9:

Determine the limit of the function as 𝑥→−2.

Q10:

Using the graph representing the function 𝑓(𝑥)=(𝑥+3)+2, determine lim→𝑓(𝑥).

Q11:

Determine the limit as 𝑥→3 of the function represented by the graph.

Q12:

Determine the limit of the function as 𝑥→−3.

Q13:

If the following graph represents the function 𝑓(𝑥)=(𝑥−1)−3, determine lim→𝑓(𝑥).

Q14:

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

Q15:

Determine lim→𝑓(𝑥).

  • A8
  • B3
  • C0
  • DThe limit does not exist.

Q16:

Find lim→𝑥−𝑥+2𝑥+7√𝑥+1 to 4 decimal places by considering 𝑓(𝑥) at 𝑥=4.1,𝑥=4.01,𝑥=4.001,…. What is the first 𝑛 that you can use?

  • A28.1744,𝑛=6
  • B28.1744,𝑛=7
  • C28.1744,𝑛=3
  • D28.1744,𝑛=5
  • E28.1744,𝑛=4

Q17:

Determine the limit of the function as 𝑥→1.

Q18:

Determine the limit of the function as 𝑥→1, if it exists.

Q19:

Determine lim→𝑓(𝑥) using the graph below.

Q20:

Find lim→𝑓(𝑥) if it exists.

  • A5
  • B−9
  • CThe limit does not exist.
  • D1

Q21:

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

Q22:

Using the following figure, determine the limit of the function as 𝑥→0.

Q23:

Determine lim→𝑓(𝑥), if it exists.

Q24:

Find lim→𝑓(𝑥).

Q25:

Determine lim→𝑓(𝑥), if it exists.

  • A−1
  • B1
  • C−2
  • DThe limit does not exist.

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