MAT-2130 Midterm: MATH 2130 App State Fall2009 Test2
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Answer key: (10 points) compute the curvature of r(t) = (t + 2, 3t + 4, 5t + 6). r (t) = (1, 3, 5) |r (t)| = 12 + 32 + 52 = 35. |r (t)| (1, 3, 5) t (t) = (0, 0, 0) |t (t)| = 0. [note: r(t) is linear so, of course, its curvature is 0. : (10 points) let f (x, y) = x + x2y2 y. Find the equation of the line tangent to f (x, y) = 1 at the point ( 1, 2). The easiest way to nd the equation of the tangent to a level curve is compute the gradient since it will give us a normal vector (a vector perpendicular to the tangent). F (x, y) = (1 + 2xy2, 2x2y 1) f ( 1, 2) = (1 + 2( 1)22, 2( 1)22 1) = ( 7, 3)
