#7 can you show me how to do this? I’ve attached a copy of my work so you can see how My teacher is teaching this. ### Evaluate the Limit**Problem Statement:**Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)\[ \lim_{{x \to 5}} \frac{{x^2 + x - 30}}{{x - 5}} \]**Answer:**-1 (Incorrect)---**Additional Materials:**- eBook---### Explanation:To solve the limit problem, we need to find the expression's limit as \(x\) approaches 5. The expression given is \(\frac{{x^2 + x - 30}}{{x - 5}}\). One common method to solve limits of rational expressions involves factoring. 1. **Factor the numerator**: Find two numbers that multiply to \(-30\) and sum to \(1\) (the coefficient of \(x\)). - The factors are \( (x - 5)(x + 6) \).2. **Rewrite the expression**: - \(\frac{{(x - 5)(x + 6)}}{{x - 5}}\).3. **Cancel the \((x - 5)\) terms**: - \(\lim_{{x \to 5}} (x + 6)\).4. **Substitute \(x = 5\)**: - \(5 + 6 = 11\).The correct limit is \(11\).If further understanding is needed, additional resources can be accessed in the eBook provided in the materials section. Below is a transcription and description for educational purposes:---### Problem Solving with Limits#### Example Problems:1. **Problem 9: Evaluate \(\lim_{x \to 4} \frac{\sqrt{x} - 2}{x - 4}\)** - **Approach**: Recognize the need to manipulate and simplify the expression. - **Step-by-step Solution**: 1. **Conjugate Method**: Multiply and divide by the conjugate \(\sqrt{x} + 2\). 2. **Simplification**: Resulting in a limit expression involving \(x - 4\) that can be cancelled. 3. **Final Calculation**: Evaluate the limit \(\lim_{x \to 4} \frac{1}{\sqrt{x} + 2} = \frac{1}{4}\). - **Note**: Additional explanation on how conjugates are used to simplify complex fractions and remove radicals in the denominator. - **Diagram**: Not depicted in this transcription, explaining cancellation of \(x - 4\).2. **Problem 10: Evaluate \(\lim_{x \to 6} \frac{\sqrt{x + 10} - 4}{x - 6}\)** - **Approach**: Use of conjugate to eliminate radicals. - **Step-by-step Solution**: 1. **Conjugate**: Multiply by \(\sqrt{x + 10} + 4\). 2. **Simplification**: Cancelling similar terms. 3. **Limit Calculation**: \(\lim_{x \to 6} \frac{1}{\sqrt{x + 10} + 4} = \frac{1}{8}\). - **Extra Notes**: Annotated explanation about middle term cancellations.3. **Additional Problems with Limits**: - **Problem 5**: \(\lim_{t \to 4} (t - 4)\) - **Solution**: Substitute \(t = 4\) directly to find \(6(4) - 4 = 38\). - **Problem 6**: \(\lim_{x \to 3} \frac{x + 3}{x + 3}\) - **Solution**: Simplification yields 1, since

Answered: Evaluate the limit, if it exists. (If…

Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 + x - 30 X - 5 lim X→5 -1 Additionol Matorials

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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