# Limits: Finding the Value of (x - Sinx) / x^3

• rambo5330
In summary, the conversation discusses the method of using L'Hopital's Rule to find the limit of (x-Sinx)/x^3 as x approaches 0, which is equal to 1/6. Other possible approaches, such as using the Maclaurin series, are mentioned but may not be applicable if the person is not familiar with L'Hopital's Rule or series.
rambo5330

## Homework Statement

lim (x->0) of (x - Sinx) / x^3

## The Attempt at a Solution

I would like to know the proper route for analyzing that question... the text is saying i should end up with 1/6 ...however I'm not sure how they arrived at that answer ...

Are you familiar with l'hopitale's rule?

if lim (x->0) a/b = 0/0 or infinity/infitity then lim (x->0) a/b = lim (x->0) a'/b'

not familiar with that yet ...

Another approach is to replace sin x by a few terms of its Maclaurin series, but if you don't know L'Hopital's Rule, you probably don't know anything about series yet, either. Short of those two techniques, I can't think of anything else that would work for you.

## 1. What is the limit of (x - Sinx) / x^3 as x approaches 0?

As x approaches 0, the limit of (x - Sinx) / x^3 is 1/6.

## 2. How do you find the limit of a function?

To find the limit of a function, you can evaluate the function as x approaches the given value. If the function is undefined at that value, you can use algebraic manipulations or L'Hopital's rule to simplify the expression and find the limit.

## 3. Can the limit of a function exist even if the function is undefined at that point?

Yes, a function can have a finite limit even if it is undefined at that point. This is known as a removable discontinuity.

## 4. What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit only considers the behavior of the function as x approaches the given value from one direction (either from the left or the right). A two-sided limit considers the behavior of the function from both directions.

## 5. How can you use a graph to determine the limit of a function?

You can use a graph to estimate the limit of a function by observing the behavior of the function as x approaches the given value. If the function approaches a specific value or has a horizontal asymptote, that value would be the limit.

Replies
19
Views
2K
Replies
5
Views
1K
Replies
12
Views
1K
Replies
5
Views
2K
Replies
13
Views
2K
Replies
11
Views
2K
Replies
8
Views
1K
Replies
8
Views
1K
Replies
24
Views
2K
Replies
12
Views
2K