Mathematics, 15.02.2021 05:30, annamerryberry1016
Let f be the function defined by f(x) = −ln(x) for 0 < x ≤ 1. R is the region between the graph of f and the x-axis.
1. This question does not permit the use of a calculator.
Determine whether region R has a finite area. If so, find the area. If not, explain why.
2. This question does not permit the use of a calculator.
Determine whether the solid generated by revolving region R about the y-axis has a finite volume. If so, find the volume. If not, explain why.
3. The formula for the arc length from a to b of a differentiable function is L equals the integral from a to b of the square root of the quantity 1 plus the square of f prime of x dx. Find the length of the curve f(x) from x = 0.5 to x = 1. Your work must show the integral, but you may use your calculator to evaluate it. Give 3 decimal places in your answer.
4. g(x) = x2. Find the area bounded by f(x), g(x) and the x-axis in the interval [0.5, 1]. Your work must show the integral, but you may use your calculator to evaluate it. Give 3 decimal places in your final answer.
5. Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares.
Your work must show the integral, but you may use your calculator to evaluate it. Give 3 decimal places for your answer.
Answers: 1
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Mathematics, 21.06.2019 23:30, aherrerasmile1
Scenario: a rectangular plot of ground is 5 meters longer than it is wide. its area is 20,000 square meters. question: what equation will you find the dimensions? note: let w represent the width. options: w(w+5)=20,000 w^2=20,000+5 (w(w+5))/2=20,000 w+2(w+5)=20,000
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