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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 53E
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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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