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Use series to evaluate the limit.

$ \lim_{x \to 0} \frac {x^3 - 3x + 3 \tan^{-1} x}{x^5} $

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$\frac{3}{5}$

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

00:52

Use series to evaluate the…

05:25

Evaluate the following lim…

04:29

01:18

you serious to be valid limit? All right, So them That's two power extra zero zero and askyou minus three x plus three are ten x over X. Well, first, expand up to the next. So this becomes too live in zero x zero and axe Cute minus three X plus three times so X minus X cubed over three, plus extra for power five or five plus some. Harold Turn off if I over six five. So become Salim as to zero and we expand this permit this and they come becomes too so three, fifty times extra power five plus some hair or the term of power five over at score file Just because two, three fifth.

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