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
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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...
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Chapter 6 / Lesson 3When 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.