Limits

• 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.
• A Sequence of Irrational Numbers with a Rational Limit
  Yes: a sequence can have only irrational terms and still converge to a rational limit, as shown by the sequence √2 divided by n.
• How to Prove a Multivariable Limit with Epsilon and Delta
  Learn the epsilon-delta definition for limits of functions of two variables and follow a worked proof using Euclidean distance and explicit bounds.
• How to Calculate the Limit of a Vector
  A vector limit is found component by component: compute each scalar limit, then combine the results, provided every component limit exists.
• 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.
• How Do Limits Resolve Zeno’s Achilles Paradox?
  Zeno’s Achilles paradox is resolved mathematically by showing that infinitely many shrinking time intervals sum to a finite limit, when motion is modeled continuously.
• How to Find Horizontal and Vertical Asymptotes Using Limits
  Horizontal asymptotes come from limits as x → ±∞; vertical asymptotes from infinite one-sided limits at a point. Step-by-step method with worked examples.