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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**Calculus: Limits**
**Problem Statement:**
Find the limit as \( x \) approaches 0 of the expression:
\[ \lim_{x \to 0} \frac{\frac{1}{x\sqrt{x+1}} - 1}{x - 1} \]
---
This problem involves finding the limit of a given expression. It appears to involve functions and understanding how they behave as \( x \) approaches a specific value. Solving this problem likely involves algebraic manipulation and possibly the use of L'Hôpital's Rule if the direct substitution results in an indeterminate form like \( \frac{0}{0} \) or \( \frac{\infty}{\infty} \).
To attempt solving this on your own:
1. Substitute the value \( x = 0 \) to check if direct substitution works.
2. If it results in an indeterminate form, apply algebraic simplification or L'Hôpital's Rule.
3. Verify all steps for continuity and validity.
For a step-by-step solution, students are encouraged to explore their notes and textbooks on limits and the appropriate rules for solving indeterminate forms.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b8b635d-64c7-420e-93b9-2c6bfd1ef1b9%2F55be9504-5be3-4cef-9fb3-76151ae073fc%2F3i0hf7r_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Calculus: Limits**
**Problem Statement:**
Find the limit as \( x \) approaches 0 of the expression:
\[ \lim_{x \to 0} \frac{\frac{1}{x\sqrt{x+1}} - 1}{x - 1} \]
---
This problem involves finding the limit of a given expression. It appears to involve functions and understanding how they behave as \( x \) approaches a specific value. Solving this problem likely involves algebraic manipulation and possibly the use of L'Hôpital's Rule if the direct substitution results in an indeterminate form like \( \frac{0}{0} \) or \( \frac{\infty}{\infty} \).
To attempt solving this on your own:
1. Substitute the value \( x = 0 \) to check if direct substitution works.
2. If it results in an indeterminate form, apply algebraic simplification or L'Hôpital's Rule.
3. Verify all steps for continuity and validity.
For a step-by-step solution, students are encouraged to explore their notes and textbooks on limits and the appropriate rules for solving indeterminate forms.
---
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