# aslino 2,2 + 2x + 8Question 3. I'm curious what range of values the function2x +1= detakes on over the interval (0, 0o). Answer my curiosity in the following steps...Part A. Show that f(z) is always decreasing over (0, 00).Part B. Use limits and the fact that f(x) is continuous on (0,oo) (you don't have to prove continuityalthough 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(a). Use those values to say whatrange of values f(z) takes on over the interval (0, oo). Hint: what does the fact that f(x) iscontinuoccur?ous and always decreasing tell you about where the largest and smallest values mustPart C. Use Mathematica or similar technology to graph f(x) over a large enough part of the interval(0, oo) to visually check that your answer to Part B is plausible.Part D. For up to 2 points of extra credit, prove that f(x) 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 5. (Based on OpenStax Calculus, Volume 1, Problem 322 in Section 4.7.)Two poles are connected by a wire that is also connected to the ground. The first pole is 20 ft tall andthe second pole is 10 ft tall. There is a distance of 30 ft between the two poles. Use Mathematica orsimilar technology to determine where the wire should be anchored to the ground in order to minimizethe amount of wire needed. See the textbook for a diagram of this situationFollow-Up

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How do you do question 4 help_outlineImage Transcriptioncloseaslino 2,2 + 2x + 8 Question 3. I'm curious what range of values the function 2x +1 = de takes on over the interval (0, 0o). Answer my curiosity in the following steps... Part A. Show that f(z) is always decreasing over (0, 00). Part B. Use limits and the fact that f(x) is continuous on (0,oo) (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(a). Use those values to say what range of values f(z) takes on over the interval (0, oo). Hint: what does the fact that f(x) is continu occur? ous and always decreasing tell you about where the largest and smallest values must Part C. U se Mathematica or similar technology to graph f(x) over a large enough part of the interval (0, oo) to visually check that your answer to Part B is plausible. Part D. For up to 2 points of extra credit, prove that f(x) 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 5. (Based on OpenStax Calculus, Volume 1, Problem 322 in Section 4.7.) Two poles are connected by a wire that is also connected to the ground. The first pole is 20 ft tall and the second pole is 10 ft tall. There is a distance of 30 ft between the two poles. Use Mathematica or similar technology to determine where the wire should be anchored to the ground in order to minimize the amount of wire needed. See the textbook for a diagram of this situation Follow-Up fullscreen
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Step 1

To find the largest-volume right circular cylinder that fits inside a sphere of radius 1. Picturize the given situation for more clarity as follows.

Step 2

Observe from the figure that:

r = the radius of base of cylinder

h = height of cylinder

From the considered right angled triangle pythagorus theorem states that:

(h/2)2r2 = 1

r2 = 1 - (h/2)2

Step 3

Thevolume of the cylinder inscribed in the sphere is

V(h) = πr2h

= πh(1- h2/4)...

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