Find \lim_{x\rightarrow 0^+} f(x) and \lim_{x\rightarrow 0^-} f(x) , where f(x) =...

Question:

Find {eq}\displaystyle \lim_{x\rightarrow 0^+} f(x) \enspace and \enspace \lim_{x\rightarrow 0^-} f(x) {/eq}, where {eq}f(x) = \left\{\begin{matrix} 2x & x \lt 0 \\ x^5 & x \geq 0 \end{matrix}\right. {/eq}

One-Sided Limits:

One-sided limits refer to limits that approach their points of evaluation only on one side.

This implies that {eq}x > c {/eq} for {eq}\displaystyle\lim_{x \rightarrow c^+} f(x) {/eq} and {eq}x < c {/eq} for {eq}\displaystyle\lim_{x \rightarrow c^-} f(x) {/eq}.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

{eq}x> 0 {/eq} for {eq}\displaystyle \lim_{x\rightarrow 0^+} f(x) {/eq} so we replace {eq}f(x) {/eq} with {eq}x^5 {/eq} as shown on the given...

See full answer below.


Learn more about this topic:

Loading...
One-Sided Limits and Continuity

from

Chapter 6 / Lesson 3
17K

When studying mathematics functions and methodology of calculation, a good place to start is by understanding the significance of one-sided limits and continuity. Learn more about properties and functions and study an example of a formula for finding one-sided limits and continuity.


Related to this Question

Explore our homework questions and answers library