# chapter 11 review.docx - Chapter 11 midterm review 11.1 1....

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Chapter 11 midterm review11.11. Express in the form y=f(x) by eliminating the parameter.x=t , y=tan1(t3+et)2. Graph the curve and draw an arrow specifying the direction corresponding to motionx=πt , y=sin(t)3. A particle follows the trajectory:x(t)=14t3+2t , y(t)=20tt2with t in seconds anddistance in centimeters.a. What is the particle’s maximum height?b. When does the particle hit the ground and how far from the origin does it land?4. Find the parametric equation for the line through P = (4, 7) of slope m = 25. Letc(t)=(3t22t ,t36t). Find:a. an equation of the tangent line at t=3.b. the points where the tangent is horizontal.11.21. Find the arc length of the path given byc(t)=(sin(3t),cos(3t))theinterval2. Find the speed of a particle with the trajectoryt(¿¿34t ,2t24t)c(t)=¿where the tangent line ishorizontal..
3. difference between arc length and displacement:4. find the surface area of the surface obtained by rotatingc(t)=(−2cosx+2.5,2sinx)aboutthe x axis on [0,3π2¿11.3

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2J, 90 degrees, 7 sec, 10J
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