Infinity

• What Happens When Infinity Is Multiplied by an Infinitesimal?
  Infinity times an infinitesimal has no single value: in limits the product may tend to zero, a finite number, or infinity.
• Can 7 Drinks with 7 Flavors Make Infinite Varieties?
  With continuously variable proportions, seven flavors produce uncountably many mathematical mixtures; counting only flavor subsets gives 127 nonempty choices.
• Find the Limit of √(9x² − x) − 3x as x → ∞
  For x tending to positive infinity, rationalize √(9x² − x) − 3x to remove the indeterminate difference and obtain the limit −1/6.