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1. Consider the parametric curve: [x = 2t y = 2t-t² 0 ≤ t ≤ 2. and the curve: y = f(x) = x³ + 4x +1, 1≤ x ≤ 3. (a) Are there any points on the parametric curve where the tangent line is horizontal? (b) Write the equation of the tangent line to the parametric curve at the point (2, 1) on the curve.

1. Consider the parametric curve: [x = 2t y = 2t-t² 0 ≤ t ≤ 2. and the curve: y = f(x) = x³ + 4x +1, 1≤ x ≤ 3. (a) Are there any points on the parametric curve where the tangent line is horizontal? (b) Write the equation of the tangent line to the parametric curve at the point (2, 1) on the curve.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the parametric curve: = 2t y = 2t - t² X = 0 ≤t≤ 2. and the curve: y = f(x) = x³ + 4x+1, 1≤ x ≤ 3. (a) Are there any points on the parametric curve where the tangent line is horizontal? (b) Write the equation of the tangent line to the parametric curve at the point (2, 1) on the curve. (c) Write an integral that represents the volume of the body of revolution generated by rotating the region in the first quadrant between the graph of y = f(x) and the x-axis about the line: x = 6. (You do not need to calculate this integral) (d) Write an integral that represents the surface area of the surface of revolution generated by rotating the graph of y = f(x) about the y-axis. (You do not need to calculate this integral)
Transcribed Image Text:1. Consider the parametric curve: = 2t y = 2t - t² X = 0 ≤t≤ 2. and the curve: y = f(x) = x³ + 4x+1, 1≤ x ≤ 3. (a) Are there any points on the parametric curve where the tangent line is horizontal? (b) Write the equation of the tangent line to the parametric curve at the point (2, 1) on the curve. (c) Write an integral that represents the volume of the body of revolution generated by rotating the region in the first quadrant between the graph of y = f(x) and the x-axis about the line: x = 6. (You do not need to calculate this integral) (d) Write an integral that represents the surface area of the surface of revolution generated by rotating the graph of y = f(x) about the y-axis. (You do not need to calculate this integral)
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