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

Question

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

Image Transcription

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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