Worksheet: Limits from Tables and Graphs

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

Q1:

Estimate l i m 𝑓 ( 𝑥 ) numerically, given that 𝑓 ( 𝑥 ) = 𝑥 2 5 𝑥 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

Q2:

Determine l i m 𝑡 0 6 𝑡 9 𝑒 9 𝑡 by evaluating the function at the following values of 𝑡 : ± 0 . 5 , ± 0 . 1 , ± 0 . 0 1 , ± 0 . 0 0 1 , and ± 0 . 0 0 0 1 .

Q3:

Determine l i m 𝑥 1 0 2 2 𝑥 + 1 0 𝑥 𝑥 1 0 0 , if it exists, by evaluating the function at the following values of 𝑥 : 9 . 5 , 9 . 9 , 9 . 9 5 , 9 . 9 9 , 9 . 9 9 9 , 9 . 9 9 9 9 , 1 0 . 5 , 1 0 . 1 , 1 0 . 0 5 , 1 0 . 0 1 , 1 0 . 0 0 1 , and 1 0 . 0 0 0 1 , rounding the result to the nearest six decimal places.

  • A0
  • B 1 2
  • C 1 0
  • DThe limit does not exist.

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 l i m 𝑓 ( 𝑥 ) .

Q7:

Given that the following graph represents the function 𝑓 ( 𝑥 ) = 𝑥 4 𝑥 + 2 , determine l i m 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 l i m 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 l i m 𝑓 ( 𝑥 ) .

Q14:

Using the graph shown, determine l i m 𝑓 ( 𝑥 ) .

Q15:

Determine l i m 𝑓 ( 𝑥 ) .

  • A0
  • B8
  • C3
  • DThe limit does not exist.

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