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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
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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This note was uploaded on 12/01/2010 for the course MAT 21B MAT 21B taught by Professor Mat21b during the Winter '07 term at UC Davis.
- Winter '07