Worksheet: Limits from Tables and Graphs

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

Q1:

Estimate lim𝑓(𝑥) numerically, given that 𝑓(𝑥)=𝑥25𝑥5.

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

Q2:

Determine lim9𝑒9𝑡 by evaluating the function at the following values of 𝑡: ±0.5, ±0.1, ±0.01, ±0.001, and ±0.0001.

Q3:

Determine lim𝑥+10𝑥𝑥100, 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 1 0
  • BThe limit does not exist.
  • C 1 2
  • D0

Q4:

Determine the limit as 𝑥1 of the function represented by the graph.

Q5:

Determine the limit as 𝑥3 of the function represented by the graph.

Q6:

If graph shown represents the function 𝑓(𝑥)=𝑥3, determine lim𝑓(𝑥).

Q7:

Given that the following graph represents the function 𝑓(𝑥)=𝑥4𝑥+2, determine lim𝑓(𝑥).

Q8:

Determine the limit of the function as 𝑥3.

Q9:

Determine the limit of the function as 𝑥2.

Q10:

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

Q11:

Determine the limit as 𝑥3 of the function represented by the graph.

Q12:

Determine the limit of the function as 𝑥3.

Q13:

If the following graph represents the function 𝑓(𝑥)=(𝑥1)3, determine lim𝑓(𝑥).

Q14:

Using the graph shown, determine lim𝑓(𝑥).

Q15:

Determine lim𝑓(𝑥).

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

Q16:

Find lim𝑥𝑥+2𝑥+7𝑥+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?

  • A 2 8 . 1 7 4 4 , 𝑛 = 6
  • B 2 8 . 1 7 4 4 , 𝑛 = 7
  • C 2 8 . 1 7 4 4 , 𝑛 = 3
  • D 2 8 . 1 7 4 4 , 𝑛 = 5
  • E 2 8 . 1 7 4 4 , 𝑛 = 4

Q17:

Determine the limit of the function as 𝑥1.

Q18:

Determine the limit of the function as 𝑥1, if it exists.

Q19:

Determine lim𝑓(𝑥) using the graph below.

Q20:

Find lim𝑓(𝑥) if it exists.

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

Q21:

Determine the limit as 𝑥2 of the function represented by the graph.

Q22:

Using the following figure, determine the limit of the function as 𝑥0.

Q23:

Determine lim𝑓(𝑥), if it exists.