Sec. 3.1

#3a) alpha(t) = (1,0)+t*(-1,1). t in [0,1]

#3d) alpha(t) = (-2,2)+t*(4,1). t in [0,0.5]

#6c) alpha(t) = theta(-cos(2pi*t),sin(2*pi*t) t in [0,0.5]

Sec. 3.2

#1a) x^2 + y^2 = 1.

#1b) y = x for x >= 0.

#1g) y = x^3 for 0 <= x <= 1.

#4d) If x = 0, then f(0,y) = |y|.

Sec. 3.3

#3a) alpha'(t) = (e^t,3*e^t), alpha'(0) = (1,3), |alpha'(0)| = sqrt(10).

#3d) alpha'(t) = (0,1,t/sqrt(1+t^2)), alpha'(0) = (0,1,0), |alpha'(0)|=1.

#6a) alpha'(t) = (-2*sin(2t),2*cos(2t)), alpha'(pi/4) = (-2,0) beta(t) = (1,3) + t*(-2,0).

#6d) alpha'(t) = (2cos(2t)*cos(t)-2t*sin(2t)*sin(t),2cos(2t)*sin(t)+ (2+sin(2t))cos(t), -3sin(3t)), alpha'(0) = (2,2,0), beta(t) = (2,0,1)+t(2,2,0).

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Last modified: Fri Oct 25 15:33:39 1996