Vertical Lines of x=5 & x=0 in y=ln(x-5)/x

In summary, the vertical lines of x=5 and x=0 in the function y=ln(x-5)/x represent the values of x=5 and x=0 respectively and act as vertical asymptotes in the graph. They indicate restrictions and help in understanding the function's behavior near these points. They cannot be removed or changed as they are essential in understanding the function. They also divide the domain into three parts and affect the range of the function.
  • #1
Petrus
702
0
Hello MHB,
I did find a problem in internet
\(\displaystyle y=\frac{ln(x-5)}{x}\)
they say there is a vertical line at \(\displaystyle x=5\) but should there not also be a vertical line at \(\displaystyle x=0\)?

Regards,
\(\displaystyle |\pi\rangle\)
 
Physics news on Phys.org
  • #2
Petrus said:
Hello MHB,
I did find a problem in internet
\(\displaystyle y=\frac{ln(x-5)}{x}\)
they say there is a vertical line at \(\displaystyle x=5\) but should there not also be a vertical line at \(\displaystyle x=0\)?

Regards,
\(\displaystyle |\pi\rangle\)

\(\displaystyle \ln(x-5) \) is undefined at $x=0$ actually the function cannot get closer to this line.
 

Related to Vertical Lines of x=5 & x=0 in y=ln(x-5)/x

1. What are vertical lines of x=5 and x=0 in y=ln(x-5)/x?

Vertical lines of x=5 and x=0 in y=ln(x-5)/x are two vertical lines on a graph that represent the values of x=5 and x=0 respectively in the equation y=ln(x-5)/x. These lines are important in understanding the behavior of the function and its asymptotes.

2. How do the vertical lines of x=5 and x=0 affect the graph of y=ln(x-5)/x?

The vertical lines of x=5 and x=0 act as vertical asymptotes for the graph of y=ln(x-5)/x. This means that the function cannot be evaluated at these points and the graph will approach but never touch these lines.

3. What is the significance of the vertical lines of x=5 and x=0 in y=ln(x-5)/x?

The vertical lines of x=5 and x=0 in y=ln(x-5)/x are important because they indicate the restrictions of the function. They also help in understanding the behavior of the function near these points.

4. Can the vertical lines of x=5 and x=0 be removed or changed in the graph of y=ln(x-5)/x?

No, the vertical lines of x=5 and x=0 cannot be removed or changed in the graph of y=ln(x-5)/x as they represent the values of x=5 and x=0 respectively in the equation and are essential in understanding the behavior of the function.

5. How do the vertical lines of x=5 and x=0 affect the domain and range of the function y=ln(x-5)/x?

The vertical lines of x=5 and x=0 divide the domain of the function into three parts: (-∞,0), (0,5), and (5,∞). The range of the function is also affected as it cannot take on values at x=5 and x=0. The range of the function is (-∞,∞) with the exception of y=0, which is not in the range.

Similar threads

B Calculating shaded area: I'm getting discrepancies between methods
    • Calculus
Replies
3
Views
393
B Why is this definite integral a single number?
    • Calculus
Replies
20
Views
2K
B Mean-Value Theorem, Taylor's formula, and error estimation
    • Calculus
Replies
3
Views
1K
I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
    • Calculus
Replies
9
Views
917
I Why is the integral of ##\arcsin(\sin(x))## so divisive?
    • Calculus
Replies
3
Views
1K
B Having trouble deriving the volume of an elliptical ring toroid
    • Calculus
Replies
4
Views
446
MHB -apc.2.1.06 crosses the x-axis at one point in the interval [0,1]
    • Calculus
Replies
4
Views
901
B Learn 0^0 w/ Young Aussie of the Year: Calculus & Real Analysis Explained
    • Calculus
Replies
14
Views
1K
MHB Volume of Solid Revolving Region About Line: 32pi/5
    • Calculus
Replies
1
Views
2K
I Explanation and clarifications in epsilon-delta limit proofs
    • Calculus
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top