Use l'Hopital's Rule to evaluate the limit. lim X- 00 4x 3/2

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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Don't understand how I got it wrong.

**Problem:**
Use l'Hopital's Rule to evaluate the limit.

\[
\lim_{{x \to \infty}} \left(\sqrt{x^2 + 4x - x}\right)
\]

**Answer Options:**

- \( \circ \) 4
- \( \circ \) 0
- \( \circ \) \(\frac{3}{2}\)
- \( \bullet \) 2

The highlighted option is 2. 

**Explanation:**
To solve this limit using l'Hopital's Rule, you first need to simplify and set the expression into a form where the rule can be applied (typically \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\)). However, in this case, the expression under the square root can be directly simplified to make the limit straightforward without needing l'Hopital's Rule.
Transcribed Image Text:**Problem:** Use l'Hopital's Rule to evaluate the limit. \[ \lim_{{x \to \infty}} \left(\sqrt{x^2 + 4x - x}\right) \] **Answer Options:** - \( \circ \) 4 - \( \circ \) 0 - \( \circ \) \(\frac{3}{2}\) - \( \bullet \) 2 The highlighted option is 2. **Explanation:** To solve this limit using l'Hopital's Rule, you first need to simplify and set the expression into a form where the rule can be applied (typically \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\)). However, in this case, the expression under the square root can be directly simplified to make the limit straightforward without needing l'Hopital's Rule.
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