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10 Nov 2019
Please answer all parts and fully explain for 5 stars!
Gabriel's Horn All parts of this problem are based on the function f(x) =1/x2/3 Find an expression for the area between f(x) and the x-axis for x = 1 to x = for some constant > 1. Take the limit as rightarrow infinity of your answer to (1) to find the area under the curve f(x) for x- values from 1 to infinity. Find the volume of the solid formed by rotating the region bounded by f(x) and the x-axis around the x-axis for x-values 1 x , for some constant > 1. Take the limit as rightarrow infinity of your answer to (3) to find the volume of this infinitely long "trumpet" (known as Gabriel's Horn). How can your results to (2) and (4) both be true? Explain.
Please answer all parts and fully explain for 5 stars!
Gabriel's Horn All parts of this problem are based on the function f(x) =1/x2/3 Find an expression for the area between f(x) and the x-axis for x = 1 to x = for some constant > 1. Take the limit as rightarrow infinity of your answer to (1) to find the area under the curve f(x) for x- values from 1 to infinity. Find the volume of the solid formed by rotating the region bounded by f(x) and the x-axis around the x-axis for x-values 1 x , for some constant > 1. Take the limit as rightarrow infinity of your answer to (3) to find the volume of this infinitely long "trumpet" (known as Gabriel's Horn). How can your results to (2) and (4) both be true? Explain.
Jarrod RobelLv2
7 Feb 2019