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Question 2. (OpenStax Calculus, Volume 1, section 4.6, exercise 294)Find3a3 -2limQuestion 3. I'm curious what range of values the function2c+1takes 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 toshow that there is no largest (and/or no smallest) value of f(x). Use those values to say whatrange of values f(x) takes on over the interval (0,00). Hint: what does the fact that f(x) iscontinuous and always decreasing tell you about where the largest and smallest values mustoccur?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.Part 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 adiagram 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
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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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Step 1

To investigate the existence of global extremum values of the function f(x) on the open interval (0,infinity)

Step 2

The essential point is that we are concerned with the values of f(x) on the OPEN interval (0,infinity). {to stress again, the point x=0 is not in the domain}. This is  in contrast to the theorem that a continuous function has to attain maximum and minimum values on a closed , bounded interval . A continuous function on an open interval need not attain a maximum or minimum value . The given function f(x) defined on (0,infinity) is such a function,

Step 3

We will use 1) , 2) and 3) to show that f(x) attains ...

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