https://r2.erweima.ai/mathbot/image/1724151189198auvi5j6s.jpg

The image shows the problem:

\[
\text{CALCULAR} \lim_{{x \to -1}} \frac{\sqrt{x^2 - x}}{5}
\]

To solve this limit, we first substitute \( x = -1 \) directly into the expression.

### Step 1: Substitute \( x = -1 \)
\[
\lim_{{x \to -1}} \frac{\sqrt{x^2 - x}}{5} = \frac{\sqrt{(-1)^2 - (-1)}}{5}
\]

### Step 2: Simplify inside the square root
\[
(-1)^2 = 1 \quad \text{and} \quad -(-1) = 1
\]
So,
\[
\sqrt{1 + 1} = \sqrt{2}
\]

### Step 3: Simplify the fraction
\[
\frac{\sqrt{2}}{5}
\]

So, the limit is:

\[
\lim_{{x \to -1}} \frac{\sqrt{x^2 - x}}{5} = \frac{\sqrt{2}}{5}
\]

Would you like further details or have any questions?

Here are some related questions:
1. How would the limit change if we approach a different value of \( x \)?
2. What are some strategies for handling square roots in limit problems?
3. How does the concept of one-sided limits apply to square root functions?
4. What are the general steps to simplify expressions under square roots?
5. How do limits involving radicals compare to polynomial limits?

**Tip:** When dealing with square roots in limits, always check the expression inside the root first to ensure it’s non-negative, especially when evaluating at or near the point of interest.

Learn how to evaluate the limit of sqrt(x^2 - x)/5 as x approaches -1 with a detailed step-by-step solution. This problem involves limits and square roots, exploring fundamental limit laws. Suitable for advanced high school or college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation