# Find Asymptotes of f(x)= 1/1+e^3x - Answers

• Starrrrr
In summary: We know that ##\huge{\lim_{x \to \infty}} 1 + e^{3x} = \infty## and ##\lim_{x \to -\infty} 1 + e^{3x} = 0##, So the positive horizontal asymptote should be 0 and negative horizontal asymptote is 1.
Starrrrr
1. Find all asymptotes of the graph of f(x).
f(x)= 1/1+e^3x

2. dy/dx= vdu/dx-udv/dx/v^2

3. Vertical asymptotes:
1+e^3x=0
3xIne=-1
X=-1/3
Horizontal asymptotes:
No horizontal asymptotes

Slant asymptotes:
None
Are the asymptotes I found correct?
Also I was wondering how can I get the first derivative of f(x) ?

Last edited by a moderator:
Starrrrr said:
Horizontal asymptotes:
No horizontal asymptotes
How would you find horizontal asymptotes?
Starrrrr said:
1+e^3x=0
3xIne=-1
That step is wrong. Try it again. If you can't spot the error, try it in smaller steps.

Starrrrr said:
1. Find all asymptotes of the graph of f(x).
f(x)= 1/1+e^3x
Surely you don't mean ##f(x) = \frac 1 1 + e^{3x}##, even though that's what you wrote.
As text, write this as f(x) = 1/(1 + e^(3x))

Also, if you intend to find the derivative, this is not a precalculus problem, so I'm moving it from the Precalc section to the Calculus & Beyond section.
Starrrrr said:
2. dy/dx= vdu/dx-udv/dx/v^2
Use parentheses! This is NOT the quotient rule.
Starrrrr said:
3. Vertical asymptotes:
1+e^3x=0
3xIne=-1
X=-1/3
Horizontal asymptotes:
No horizontal asymptotes
No, this is incorrect.
Starrrrr said:
Slant asymptotes:
None
Are the asymptotes I found correct?
Also I was wondering how can I get the first derivative of f(x) ?
The most obvious way is to use the quotient rule. There's another way that might be simpler, that uses the chain rule.

Mark44 said:
Surely you don't mean ##f(x) = \frac 1 1 + e^{3x}##, even though that's what you wrote.
As text, write this as f(x) = 1/(1 + e^(3x))

Also, if you intend to find the derivative, this is not a precalculus problem, so I'm moving it from the Precalc section to the Calculus & Beyond section.
Use parentheses! This is NOT the quotient rule.
No, this is incorrect.

The most obvious way is to use the quotient rule. There's another way that might be simpler, that uses the chain rule.
I got it now , there are no vertical asymptotes. Horizontal asymptotes as x tends to infinity 1/(1+e^(3x)) = 1and negative infinity is 0

And also I have to use the chain rule

Starrrrr said:
I got it now , there are no vertical asymptotes. Horizontal asymptotes as x tends to infinity 1/(1+e^(3x)) = 1and negative infinity is 0
No, it is incorrect.
We know that ##\huge{\lim_{x \to \infty}} 1 + e^{3x} = \infty## and ##\lim_{x \to -\infty} 1 + e^{3x} = 0##, So the positive horizontal asymptote should be 0 and negative horizontal asymptote is 1.

## 1. What is an asymptote?

An asymptote is a line or curve that a graph approaches but never touches, even as the input values approach infinity or negative infinity.

## 2. How do I find the asymptotes of a function?

To find the asymptotes of a function, you can start by simplifying the function and looking for any discontinuities or undefined points. Then, you can use the limit definition of asymptotes to determine the vertical and horizontal asymptotes.

## 3. What is the difference between vertical and horizontal asymptotes?

A vertical asymptote is a vertical line that a graph approaches but never touches, while a horizontal asymptote is a horizontal line that a graph approaches but never crosses. Vertical asymptotes occur when the function has a value that is undefined, while horizontal asymptotes occur when the input values approach infinity or negative infinity.

## 4. How do I use the limit definition of asymptotes to find the asymptotes of a function?

The limit definition of asymptotes involves taking the limit of a function as the input values approach a certain value, typically infinity or negative infinity. For vertical asymptotes, you would set the denominator of the function equal to zero and solve for the input value that makes it undefined. For horizontal asymptotes, you would take the limit of the function as the input values approach infinity or negative infinity.

## 5. Can a function have more than one asymptote?

Yes, a function can have multiple asymptotes. It can have both vertical and horizontal asymptotes, as well as more than one of each type. The number and type of asymptotes a function has depends on the behavior of the function as the input values approach infinity or negative infinity.

Replies
25
Views
1K
Replies
2
Views
735
Replies
3
Views
967
Replies
4
Views
992
Replies
3
Views
1K
Replies
4
Views
1K
Replies
4
Views
1K
Replies
24
Views
2K
Replies
16
Views
2K
Replies
5
Views
1K