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Worksheet: L’Hôpital's Rule: ∞/∞

Q1:

Given functions 𝑓 and 𝐹 , that are positive for large values of 𝑥 , we say that 𝐹 dominates 𝑓 as 𝑥 if

Use l’Hôpital's Rule to decide which is dominant as 𝑥 : l n 𝑥 or 𝑥 .

  • A 𝑥 dominates l n 𝑥 .
  • B l n 𝑥 dominates 𝑥 .

Q2:

Determine l i m 𝑥 2 𝑥 2 𝑥 2 𝑥 2 𝑥 5 𝑒 3 𝑒 3 𝑒 4 𝑒 .

  • A0
  • B
  • C 3 4
  • D 5 3
  • E 2

Q3:

Find l i m 𝑥 3 𝑥 3 𝑥 2 𝑒 5 3 𝑒 1 .

  • A 2
  • B
  • C5
  • D 2 3
  • E 5 3

Q4:

Determine