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Worksheet: Graphical Estimation of Limits at Infinity

Q1:

Consider the graph of 𝑓 ( π‘₯ ) = 2 ( 4 π‘₯ ) π‘₯ s i n .

Estimate l i m π‘₯ β†’ βˆ’ ∞ 𝑓 ( π‘₯ ) .

Estimate l i m π‘₯ β†’ ∞ 𝑓 ( π‘₯ ) .

  • A0
  • B βˆ’ ∞
  • C ∞
  • DThe limit does not exist.

Q2:

Consider the graph of 𝑓 ( π‘₯ ) = 𝑒 π‘₯ π‘₯ .

Estimate l i m π‘₯ β†’ βˆ’ ∞ 𝑓 ( π‘₯ ) .

Estimate l i m π‘₯ β†’ ∞ 𝑓 ( π‘₯ ) .

  • AThe limit does not exist.
  • B0
  • C βˆ’ ∞
  • D ∞

Q3:

Consider the function 𝑓 ( π‘₯ ) = 1 π‘₯ βˆ’ 6 2 whose graph is shown.

Complete the table of values. Give exact answers.

π‘₯ 10 100 1 000 10 000
𝑓 ( π‘₯ )
  • Aβˆ’5.9, βˆ’5.99, βˆ’5.999, βˆ’5.9999
  • Bβˆ’5.95, βˆ’5.995, βˆ’5.9995, βˆ’5.99995
  • C6.01, 6.0001, 6.000001, 6.00000001
  • Dβˆ’5.99, βˆ’5.9999, βˆ’5.999999, βˆ’5.99999999

Hence, estimate l i m π‘₯ β†’ ∞ 𝑓 ( π‘₯ ) .