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Worksheet: Limits: Evaluation from Tables and Graphs

In this worksheet, we will practice finding limits of functions from graphs and tables of values.

Q1:

Use the graph shown to find l i m π‘₯ β†’ βˆ’ 3 + 𝑓 ( π‘₯ ) .

Q2:

Use the graph shown to find l i m π‘₯ β†’ 1 + 𝑓 ( π‘₯ ) .

Q3:

Use the graph shown to find l i m π‘₯ β†’ 4 + 𝑓 ( π‘₯ ) .

Q4:

Use the graph below to find l i m π‘₯ β†’ 3 βˆ’ 𝑓 ( π‘₯ ) .

Q5:

Use the graph below to find l i m π‘₯ β†’ 2 βˆ’ 𝑓 ( π‘₯ ) .

Q6:

Determine l i m π‘₯ β†’ 4 𝑓 ( π‘₯ ) , if it exists.

Q7:

Determine l i m π‘₯ β†’ βˆ’ 3 𝑓 ( π‘₯ ) , if it exists.

Q8:

Find l i m π‘₯ β†’ βˆ’ 3 𝑓 ( π‘₯ ) .

Q9:

Find l i m π‘₯ β†’ βˆ’ 2 𝑓 ( π‘₯ ) .

Q10:

Estimate l i m π‘₯ β†’ βˆ’ 2 𝑓 ( π‘₯ ) from the given table.

π‘₯ βˆ’ 2 . 1 βˆ’ 2 . 0 1 βˆ’ 2 . 0 0 1 ⟢ βˆ’ 2 ⟡ βˆ’ 1 . 9 9 9 βˆ’ 1 . 9 9 βˆ’ 1 . 9
𝑓 ( π‘₯ ) 36.9 36.09 36.009 ⟢ ⟡ 35.991 35.91 35.1

Q11:

Estimate l i m π‘₯ β†’ 5 𝑓 ( π‘₯ ) numerically, given that 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 2 5 π‘₯ βˆ’ 5 2 .

π‘₯ 4.9 4.99 4.999 ⟢ 5 ⟡ 5.001 5.01 5.1
𝑓 ( π‘₯ ) 9.8 9.98 9.998 ⟢ ⟡ 10.002 10.02 10.2

Q12:

Determine l i m π‘₯ β†’ βˆ’ 1 0 2 2 βˆ’ π‘₯ + 1 0 π‘₯ π‘₯ βˆ’ 1 0 0 , if it exists, by evaluating the function at the following values of π‘₯ : βˆ’ 9 . 5 , βˆ’ 9 . 9 , βˆ’ 9 . 9 5 , βˆ’ 9 . 9 9 , βˆ’ 9 . 9 9 9 , βˆ’ 9 . 9 9 9 9 , βˆ’ 1 0 . 5 , βˆ’ 1 0 . 1 , βˆ’ 1 0 . 0 5 , βˆ’ 1 0 . 0 1 , βˆ’ 1 0 . 0 0 1 , and βˆ’ 1 0 . 0 0 0 1 , rounding the result to the nearest six decimal places.

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

Q13:

Determine l i m 𝑑 β†’ 0 6 𝑑 9 𝑒 βˆ’ 9 𝑑 by evaluating the function at the following values of 𝑑 : Β± 0 . 5 , Β± 0 . 1 , Β± 0 . 0 1 , Β± 0 . 0 0 1 , and Β± 0 . 0 0 0 1 .

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