wksht17 - ESP Kouba Worksheet 17 1 Graph the curve...

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Unformatted text preview: ESP Kouba Worksheet 17 1.) Graph the curve represented by the following pairs of parametric equations. If possible, eliminate t and write an equation for the curve in rectangular coordinates. a.) x=t-1,y=t+1 b.) x=t,y=t2 c.) x—t2,y=t4 d.) x=e",y=e2t e.) x=cost,y=smt f.) x=Scost,y=smt g.) x=t2-t,y=t2 h.) x=|nt,y=t+1/t 2.) Determine the slope of the line tangent to the following graphs at the indicated value. .) =(1c—arctanx)4 at x=1 a Y b.) x=t2+1,y=e‘t+t at t=1 c.) r=3+sin6 at 9=n/4 3.) Compute dy/dx and d 2y/dx 2 for each of the following. a.) y=x/(x2+1) b.) x=t+sint,y=eta“t-t c.) r=6 d.) r=sine 4.) Consider the curve given parametrically by x=t2+etandy=t+et fortin [0,1]. Find the area of the region lying under the curve and above the x-axis for x in [1 , 1 + e] . 5.) Compute the arc lengths of the given curves over the indicated intervals. a.) y = x5/4 for x in [0,1] b.) y=1/(2x2)+x4/16 forxin [2,3] C) x=cost+tsint and y=sint-tcost for t in [men/4] d) r = sin2(e/2) for e in [0.7:] 6.) Consider a particle moving along the curve given parametrically by x=t+cost and y=t-sint for tZO. a.) Determine a formula for the speed (ft/sec.) of the particle at time t . b.) What is the speed when t=O sec. ? t= n/2 sec. ? t=1OO sec. ? 7.) Compute the curvature of the given curve at the given point. a.) y=x3 at (-1,1) b.) y=ex2 at (1,e) c.) x=t2-t,y=t2+t att=1 ...
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  • Spring '07
  • MAT21B
  • Parametric equation, following pairs, Rectangular Coordinates, Compute dy/dx

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