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

Problem

ƒ(x)=ln(x)

Solution

1. Identify the domain of the function. The natural logarithm function ƒ(x)=ln(x) is defined only for x>0

2. Check for vertical asymptotes by evaluating the limit as x approaches the boundary of the domain from the right.

3. Evaluate the limit (lim_x→0)(ln(x)) As x approaches 0 from the positive side, ln(x) approaches −∞

4. Determine the vertical asymptote based on the limit. Since the function approaches −∞ as x→0 there is a vertical asymptote at x=0

5. Check for horizontal asymptotes by evaluating the limit as x approaches ∞

6. Evaluate the limit (lim_x→∞)(ln(x)) As x increases without bound, ln(x) also increases without bound, so there are no horizontal asymptotes.

Final Answer

Vertical Asymptote: *x=0

Want more problems? Check here!