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Worksheet: Applying L’Hôpital's Rule for Limits with ∞/∞ Output

Q1:

Determine

Q2:

Given functions and , that are positive for large values of , we say that dominates as provided that

Use L'Hopital's rule to decide which is dominant as between and .

  • A dominates .
  • B dominates .

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 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