Answered: The natural logarithmic function f(x) =…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.3: Logarithmic Functions

Problem 5E: The natural logarithmic function f(x)=Inx has the ____________ asymptote x =____.

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Related questions

Question

The natural logarithmic function f(x) = In x has the
asymptote x =

Expert Solution

Step 1

Given:

$f (x) = \ln x$

To Find:

$Asymptote of f (x) .$

Concept:

$Vertical Asymptote: x = c is called vertical asymptote of f (x) if either \lim_{x \to c} f (x) = \infty or \lim_{x \to c} f (x) = - \infty . Horizontal Asymptote: y = L is called horizontal asymptote of y = f (x) if either \lim_{x \to \infty} f (x) = L or \lim_{x \to - \infty} f (x) = L, w h e r e L is defined and finite .$

Step 2

Explanation:

$Vertical Asymptote: \lim_{x \to 0} f (x) = \lim_{x \to 0} \ln x = - \infty \Rightarrow x = 0, is a vertical Asymptote of f (x) = \ln x . Horizontal Asymptote: \lim_{x \to \infty} f (x) = \lim_{x \to \infty} \ln x = \infty Hence, f (x) = \ln x has no horizontal asymptote:$