Calculus 1000A/B Lecture Notes - Lecture 2: Asymptote

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Rasul Shafikov

Document Summary

If we try direct substitution we get n n + 1 lim n . If we write out the first few terms and look for a pattern we get: From inspection is seems that n n + 1 lim n . When evaluating the limit of an infinite sequence we make use of the following identity lim n . Re-doing the above question using this property: lim n n n + 1. Note: the technique here is to divide through by the highest power of n. In this example we will divide through by n 2 . Note: we can also apply this reasoning to functions. Consider the function defined by f (x) = As x becomes infinitely large, f(x) gets closer and closer to the value. Another useful property: lim r n = 0, r < 1 n . Infinite series r < 1, the infinite geometric series.