Find the Asymptotes f(x) = natural log of x+1

Problem

ƒ(x)=ln(x+1)

Solution

1. Identify the domain of the function by setting the argument of the natural logarithm to be greater than zero.

x+1>0

2. Solve for x to find the boundary of the domain.

x>−1

3. Determine the vertical asymptote by finding the value of x where the argument of the natural logarithm approachs zero from the right.

(lim_x→−1)(ln(x+1))=−∞

4. Check for horizontal asymptotes by evaluating the limit of the function as x approaches infinity.

(lim_x→∞)(ln(x+1))=∞

5. Conclude that there are no horizontal asymptotes because the limit does not approach a finite constant.

Final Answer

Vertical Asymptote: *x=−1

Want more problems? Check here!