Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
8) find the limit
![**Title: Understanding Limits in Calculus**
**Date: January 10th, 2022**
**Content:**
On this page, we explore the concept of limits in calculus. The specific limit we are evaluating is:
\[
\lim_{{x \to \sqrt[3]{5}}} \left( \frac{x^2}{5} - \frac{1}{x} \right)
\]
This expression involves calculating the limit of a function as \(x\) approaches the cube root of 5. The function comprises two parts:
1. \(\frac{x^2}{5}\): This term represents a quadratic function divided by a constant.
2. \(-\frac{1}{x}\): This term is a rational function, which inversely depends on \(x\).
The task is to analyze the behavior of this combined function as \(x\) approaches \(\sqrt[3]{5}\).
Understanding and solving such limits is a foundational skill in calculus, providing insight into the continuity and behavior of functions near particular points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb034729f-db63-4235-9b33-79c3c77be50a%2F99a98ddd-e67f-4ce2-a754-1f70ebf7e610%2Fl8i3lqh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Limits in Calculus**
**Date: January 10th, 2022**
**Content:**
On this page, we explore the concept of limits in calculus. The specific limit we are evaluating is:
\[
\lim_{{x \to \sqrt[3]{5}}} \left( \frac{x^2}{5} - \frac{1}{x} \right)
\]
This expression involves calculating the limit of a function as \(x\) approaches the cube root of 5. The function comprises two parts:
1. \(\frac{x^2}{5}\): This term represents a quadratic function divided by a constant.
2. \(-\frac{1}{x}\): This term is a rational function, which inversely depends on \(x\).
The task is to analyze the behavior of this combined function as \(x\) approaches \(\sqrt[3]{5}\).
Understanding and solving such limits is a foundational skill in calculus, providing insight into the continuity and behavior of functions near particular points.
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