Question

17. If $f$ is a real-valued function on $(0, \infty)$ and if \\ $g(x) = f(\frac{1}{x}) \qquad (0 < x < \infty)$, \\ prove that $\lim_{x \to \infty} f(x) = L$ if and only if $\lim_{x \to 0^+} g(x) = L$.

          17. If $f$ is a real-valued function on $(0, \infty)$ and if \\
$g(x) = f(\frac{1}{x}) \qquad (0 < x < \infty)$, \\
prove that $\lim_{x \to \infty} f(x) = L$ if and only if $\lim_{x \to 0^+} g(x) = L$.

17. If f is a real-valued function on (0, ∞) and if

g(x) = f((1)/(x)) (0 < x < ∞),

prove that limx →∞ f(x) = L if and only if limx → 0^+ g(x) = L.

Added by James G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

05/10/2022

Step 1

Step 1: Assume that limx->0+ g(x) = L. Show more…

Show all steps

Thanks for your feedback!

17. If f is a real-valued function on (0,co) and if g(x)=f( (c>x>0) prove that limx- f(x)= L if and only if lim-0+ g(x)= L.

Play audio

Feedback

Shaiju T and 95 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later

Question

17. If $f$ is a real-valued function on $(0, \infty)$ and if \\ $g(x) = f(\frac{1}{x}) \qquad (0 < x < \infty)$, \\ prove that $\lim_{x \to \infty} f(x) = L$ if and only if $\lim_{x \to 0^+} g(x) = L$.

Please give Ace some feedback