Calculus Limits Study Note 7

Summary:

Differential calculus is a branch of calculus that deals with the concept of a derivative, representing the rate of change of a quantity. One of the fundamental topics in differential calculus is the concept of a limit. This study note explores the concept of limits and various related topics.

In the previous study note, we learned about the different types of functions and their properties essential for understanding the relationship between independent and dependent variables. In this study note, we begin our journey into calculus with the concept of limits.

We start with the concept of an infinite sequence, which is a sequence that has no ending term. A formula with a variable defines an infinite sequence, n, that takes on specific values like 1, 2, 3, and so on. We use the formula to generate the terms of the sequence.

Next, we discuss a function’s limit, denoted by lim (x → a) f(x). It represents the value that a function approaches as its input (x) gets arbitrarily close to a certain value (a). We provide examples to illustrate the concept of limits and how to evaluate them.

We also introduce left-sided and right-sided limits. The left-sided limit, lim (x → a-) f(x), represents the value the function approaches as x approaches a from the left. The right-sided limit, lim (x → a+) f(x), represents the value the function approaches as x approaches a from the right. If both the left-sided and right-sided limits are equal and exist, then the overall limit exists and is equal to that common value.

Excerpt:

Calculus Limits Study Note 7

In the last StudyNote 6, we learned the most important topic in Calculus: the different types of functions. We have studied the properties of functions that are essential to determine the relationship between the independent and dependent variables. In this StudyNote 7, we will learn the first topic in Calculus, which is all about limits.

INFINITE SEQUENCE
An infinite sequence is a type of sequence with unending terms. Meaning this is a sequence with no ending term.