Section 7.4 Reading Assignment: Relative Rates of Growth

Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions very carefully and see on what it is asking for and what is really about. Please be careful with this assignment.

References: Thomas' Calculus: Early Transcendentals | Calculus | Calculus | Mathematics | Store | Pearson+

Feedback: #1: What exactly is being compared when we consider the limit of this fraction based on the reading? (0/2) #2: Reconsider this one based on the reading, especially the numerical result. (1/2) #3: Rephrase this one and reconsider the process considered in this reading. (1/2).

Section 7.4 Reading Assignment: Relative Rates of Growth1 Instructions. Read through this assignment and complete the three exercises below based on this reading. In Chapter 10, we will encounter lots of different limits as n - co. Fortunately for us, limits at infinity will be the only ones we're concerned with in this chapter, but there is a lot going on with these limits and some intuition that it'd be good to develop about these limits. Hopefully you remember L'Hopital's rule and the fact that - is an indeterminate form, meaning that its value depends on the particulars of the problem. This illustrates that the use of the infinity symbol as a single quantity actually removes a lot of information about a limit. To take an example, while both 3n and n' approach co (as n - co), n is, in a sense, faster than 3n. This can be seen when taking the limit of the fraction lim 3n = lim - = 0. This is what I meant before: there are many different speeds that n+00 n2 n+00 n we can approach infinity, so - can have any value (including infinity). In lim = = 0, the expressions 3n and n' are "racing" with each other: 3n in the numerator is pulling the limit closer to infinity, while n in the denominator is pulling the limit closer to zero. The result shows n completely won that race. In other cases, there's something like a tie in the race, which we will explore later. We take this as an inspiration for defining what we mean by one sequence growing faster than another: Definition. A sequence an is growing slower than another sequence by which is written an