Answered: Question 2. (OpenStax Calculus, Volume…

Generalizing the washer method | Applications of definite integrals | AP Calculus AB | Khan Academy
Generalizing the washer method | Applications of definite integrals | AP Calculus AB | Khan Academy

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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ISBN: 9781337111348

Author: Bruce Crauder, Benny Evans, Alan Noell

Publisher: Cengage Learning

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How do you do part b to question 3

Question 2. (OpenStax Calculus, Volume 1, section 4.6, exercise 294) Find 3a3 -2 lim Question 3. I'm curious what range of values the function 2c+1 takes on over the interval (0, 00). Answer my curiosity in the following steps... Part A. Show that f (x) is always decreasing over (0, oo). Part B. Use limits and the fact that f(x) is continuous on (0, 00) (you don't have to prove continuity, although see Part D below) to find the largest and smallest values that f (x) takes on, or to show that there is no largest (and/or no smallest) value of f(x). Use those values to say what range of values f(x) takes on over the interval (0,00). Hint: what does the fact that f(x) is continuous and always decreasing tell you about where the largest and smallest values must occur? Part C. Use Mathematica or similar technology to graph f(x) over a large enough part of the interval (0, 0o) to visually check that your answer to Part B is plausible. Par t D. For up to 2 points of extra credit, prove that f(a) really is continuous on the interval (0, 00). Question 4. (Based on OpenStax Calculus, Volume 1, Problem 341 in Section 4.7.) Find the largest-volume right circular cylinder that fits inside a sphere of radius 1. Start by drawing a diagram of the situation

Transcribed Image Text:Question 2. (OpenStax Calculus, Volume 1, section 4.6, exercise 294) Find 3a3 -2 lim Question 3. I’m curious what range of values the function 2c+1 takes on over the interval (0, 00). Answer my curiosity in the following steps… Part A. Show that f (x) is always decreasing over (0, oo). Part B. Use limits and the fact that f(x) is continuous on (0, 00) (you don’t have to prove continuity, although see Part D below) to find the largest and smallest values that f (x) takes on, or to show that there is no largest (and/or no smallest) value of f(x). Use those values to say what range of values f(x) takes on over the interval (0,00). Hint: what does the fact that f(x) is continuous and always decreasing tell you about where the largest and smallest values must occur? Part C. Use Mathematica or similar technology to graph f(x) over a large enough part of the interval (0, 0o) to visually check that your answer to Part B is plausible. Par t D. For up to 2 points of extra credit, prove that f(a) really is continuous on the interval (0, 00). Question 4. (Based on OpenStax Calculus, Volume 1, Problem 341 in Section 4.7.) Find the largest-volume right circular cylinder that fits inside a sphere of radius 1. Start by drawing a diagram of the situation

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