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.

Answered: Image /qna-images/answer/ad7b57e0-cbd3-4cfa-8791-9c19c9d671e1.jpg

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

Math

Calculus

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

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...

See similar textbooks

Similar questions

help
please solve it as soon as possible
Please show every step. Do NOT skip a step as it is hard to follow when steps are skipped.
Need to find 3 meanings.
formulate 2 examples of compound statements under disjunction
Instructions: Every item is composed of two statements about RESEARCH. Read and analyze the statements carefully whether they are true or not. Choose your answer from the box and write your answers on the space provided after all the items. А- The statement X is correct. С- Both statements X and Y are correct. В- The statement Y is correct. D- Both statements X and Y are wrong.
Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly A microbiologist measures the distance across a red blood cell and an astronomer measures the distance across the Milky Way galaxy. The absolute error that the microbiologist makes in measuring the cell must be less than the absolute error that the astronomer makes in measuring the Milky Way. Choose the correct answer below. A. The statement makes sense. The absolute error in the cell measurement must be very small in comparison to the absolute error in the measurement of the Milky Way, which is likely to be very large. O B. The statement makes sense. The absolute error in the cell measurement must be negative while the error in the measurement of the Milky Way must be positive. O C. The statement does not make sense. The absolute error is computed by dividing the error by the true value. Since the cell measurement is a small value, the absolute error is likely…
PRACTISING 4. Simplify. State any restrictions on the variables. 5ab 15ab – 10a b?
Questic *adjA = and A = ,then x is equal to 2. Select one: O True O False