# Worksheet: Limits from Tables and Graphs

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

Q1:

Estimate numerically, given that .

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

Q2:

Determine by evaluating the function at the following values of : , , , , and .

Q3:

Determine , if it exists, by evaluating the function at the following values of : , , , , , , , , , , , and , rounding the result to the nearest six decimal places.

• A
• BThe limit does not exist.
• C
• D0

Q4:

Determine the limit as of the function represented by the graph. Q5:

Determine the limit as of the function represented by the graph. Q6:

If graph shown represents the function , determine . Q7:

Given that the following graph represents the function , determine . Q8:

Determine the limit of the function as . Q9:

Determine the limit of the function as . Q10:

Using the graph representing the function , determine . Q11:

Determine the limit as of the function represented by the graph. Q12:

Determine the limit of the function as . Q13:

If the following graph represents the function , determine . Q14:

Using the graph shown, determine . Q15:

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

Q16:

Find to 4 decimal places by considering at . What is the first that you can use?

• A
• B
• C
• D
• E

Q17:

Determine the limit of the function as . Q18:

Determine the limit of the function as , if it exists. Q19:

Determine using the graph below. Q20:

Find if it exists. • A5
• B
• CThe limit does not exist.
• D1

Q21:

Determine the limit as of the function represented by the graph. Q22:

Using the following figure, determine the limit of the function as . Q23:

Determine , if it exists. Q24:

Find . Q25:

Determine , if it exists. • A
• B1
• C
• DThe limit does not exist.