Various exercises relating to orders of growth.

Use orders of growth to identify dominant terms and compute limits.
  • Compute the limit: The dominant terms are
    in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator
  • Compute the limit: The dominant terms are
    in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator
  • Compute the limit: The dominant terms are
    in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator
  • Compute the limit: The dominant terms are
    in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator in the numerator and in the denominator
  • Compute the limit:
    dominates dominates
  • Compute the limit: (First identify whether the square-root term is dominant or not; when it is dominant, identify the dominant term inside the square root and neglect the non-dominant term.)
  • Compute the limit:
  • Compute the limit
    dominantes as dominates as
  • Compute the limit:
    dominates as dominates as
  • Compute the limit:
    dominates as dominates as
  • Compute the limit: (Use the laws of exponents to write .)

Sample Quiz Questions

Arrange the functions in order from least rate of growth to greatest rate of growth as . Compare on the basis of magnitude rather than sign, i.e., if a function is negative, take its absolute value first.

Arrange the functions in order from least rate of growth to greatest rate of growth as . Compare on the basis of magnitude rather than sign, i.e., if a function is negative, take its absolute value first.

Arrange the functions in order from least rate of growth to greatest rate of growth as . Compare on the basis of magnitude rather than sign, i.e., if a function is negative, take its absolute value first.

Arrange the functions in order from least rate of growth to greatest rate of growth as . Compare on the basis of magnitude rather than sign, i.e., if a function is negative, take its absolute value first.