Page 2: Arithmetic Operations with Sequence Limits
This page delves into the rules for performing arithmetic operations with sequence limits, specifically focusing on addition, multiplication, and division. These rules are essential for solving more complex limit problems and understanding the behavior of combined sequences.
Highlight: The reguła dodawania i mnożenia ruleofadditionandmultiplication for limits is a fundamental concept in calculus.
The page begins by explaining the addition of limits:
Example: limn→∞ 1+2 = limn→∞ 1 + limn→∞ 2 = 0 + 2 = 2
This example demonstrates that the limit of a sum equals the sum of the limits.
Next, the multiplication of limits is discussed:
Example: limn→∞ 6/n⋅2/n2 = limn→∞ 6/n · limn→∞ 2/n² = 0 · 0 = 0
This illustrates how the limit of a product is equal to the product of the limits.
The page concludes with an example of limit division:
Example: limn→∞ 2n2−3n / n2+5 = 2
This complex example showcases the application of limit rules to rational functions, demonstrating how to handle indeterminate forms and simplify expressions to find the limit.
Vocabulary: Metryką Manhattan Manhattanmetric - A way of measuring distance in a grid-like path between two points.
The page provides valuable insights into obliczanie granic ciągów zbieżnych calculatinglimitsofconvergentsequences and reinforces the importance of these rules in solving advanced limit problems.
