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# 271 - MA 271 EXAM 1 FALL 2002 Name 1 Find the angle between...

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Unformatted text preview: MA 271 EXAM 1 FALL 2002 Name 1. Find the angle between the curves at the indicated point. r1(t) = (cos t)i + (sin t)i + tk, at (1,0,0). r2(t) = (1 + t)i + tzj + tetk, 2. Solve the initial value problem 2 r(0)=0, d—:(0)=i+j+k, %=t2i+tj+k 3. Find the arc length r(t) = t2i + 2tj + (lnt)k, 1 < t < e2. 4. Convert to Cartesian equation 7" : 4tan6sec0 5. Find the area of the region shared by the circles r = 2 sin0 and 7" = 2 cos 0. 6. Find the center and radius of the sphere m2+y2+zz+6x—8y+4z+4=0. 7. Find the equation for the plane through (1,1,—1), (2,0,2) and (0, —2, 1). . 8. Describe the surfaces. (a) x2 + 4y2 + 922 = 1 (b) 312 = -4x (c) 3/2 + 3:2 = 22 (d) m2+y2—z2 2—1 (e) w = yz 9. Find the equation of tangent line at time t = x/g. r(t) = (1n(t2 + 1))i+ (tan—1t)j + (W2 + 1)k 10. Let C be the intersection of 3:2 + y2 = 16 and x + y + z = 5. Find the curvature at (0,4,1). ...
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271 - MA 271 EXAM 1 FALL 2002 Name 1 Find the angle between...

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