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1. A curve in the plane is defined parametrically by: x(t) = t +1 and y(t) = t2-5t +2. a)Convert the parametric equations of the curve to an equation involving only the variables x and y. b)Using the parametric representation of the curve, find the equation (in standard x-y form) of the line tangent to the curve at the point (x(1),y(1)) on the curve. c)Using the parametric representation of the curve, find the exact area of the region beneath the curve, above the x-axis, between x = 0 and x = 1.

1. A curve in the plane is defined parametrically by: x(t) = t +1 and y(t) = t2-5t +2. a)Convert the parametric equations of the curve to an equation involving only the variables x and y. b)Using the parametric representation of the curve, find the equation (in standard x-y form) of the line tangent to the curve at the point (x(1),y(1)) on the curve. c)Using the parametric representation of the curve, find the exact area of the region beneath the curve, above the x-axis, between x = 0 and x = 1.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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1. A curve in the plane is defined parametrically by: x(t) = t +1 and y(t) = t2-5t +2. a)Convert the parametric equations of the curve to an equation involving only the variables x and y. b)Using the parametric representation of the curve, find the equation (in standard x-y form) of the line tangent to the curve at the point (x(1),y(1)) on the curve. c)Using the parametric representation of the curve, find the exact area of the region beneath the curve, above the x-axis, between x = 0 and x = 1.
Transcribed Image Text:1. A curve in the plane is defined parametrically by: x(t) = t +1 and y(t) = t2-5t +2. a)Convert the parametric equations of the curve to an equation involving only the variables x and y. b)Using the parametric representation of the curve, find the equation (in standard x-y form) of the line tangent to the curve at the point (x(1),y(1)) on the curve. c)Using the parametric representation of the curve, find the exact area of the region beneath the curve, above the x-axis, between x = 0 and x = 1.
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