A-Cshow all formulas and all steps of justification. Provide proper units **Problem 6: Analysis of Functions for Absolute Extrema**In this problem, we are tasked to determine which of the given functions has an absolute maximum and an absolute minimum on the interval \([0, 10]\). If a function does not satisfy the criteria for the Extreme Value Theorem, we must explain why.**Functions:**a) \( f(x) = \frac{\ln(x)}{x+5} \)b) \( g(x) = \frac{x^2 - 5}{x^2 + 5} \)c) \( h(x) = \frac{x^2 + 2x + 1}{x^2 - 1} \)**Guidance:**To determine if a function has an absolute maximum and minimum on a closed interval \([a, b]\), the following conditions must be checked:1. **Continuity:** The function must be continuous on the closed interval \([a, b]\).2. **Closed Interval:** The interval itself must be closed, which in this case, \([0, 10]\) already is.**Function Analysis:**- **For \( f(x) \):** Analyze the continuity of \( f(x) = \frac{\ln(x)}{x+5} \) from \(0\) to \(10\). Particularly, check any points where \( \ln(x) \) and the denominator could cause discontinuities.- **For \( g(x) \):** Check the continuity of \( g(x) = \frac{x^2 - 5}{x^2 + 5} \) over \([0, 10]\). Evaluate if the denominator \(x^2 + 5\) introduces any discontinuity.- **For \( h(x) \):** Inspect \(\frac{x^2 + 2x + 1}{x^2 - 1}\) for intervals where discontinuities may occur, particularly where the denominator could become zero.**Conclusion:**- Possible discontinuities should be noted for functions where the denominator equals zero or where logarithmic functions are undefined (e.g., \(\ln(x)\) at \(x = 0\)). This information helps in assessing continuity and the applicability of the Extreme Value Theorem.

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Answered: A-C show all formulas and all steps of…

A-C show all formulas and all steps of justification. Provide proper units

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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