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This 3 page Class Notes was uploaded by Mike Orn on Tuesday October 20, 2015. The Class Notes belongs to MATH102 at Solano Community College taught by DorothyHawkes in Fall. Since its upload, it has received 9 views. For similar materials see /class/225398/math102-solano-community-college in Mathematics (M) at Solano Community College.
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Date Created: 10/20/15
Math 22 Review 133 152 Unit tangent vector Tt 1J0 Unit normal vector Nt Tia r39tl T39U Binormal vector Tt gtlt Nt v t a t 2 r39t gtlt rquott aT v t where vt vt and aN Kvt TH 1 Suppose that the position of a particle after t seconds is given by m lt3sin2t 5cos2t 4sin2tgt a Find the speed of the particle after 11 seconds b Find the unit tangent vector when t 11 c Find the acceleration vector when t 11 d Find the unit normal vector when t 11 e Find the tangential component of the acceleration vector when t 11 e Find the normal component of the acceleration vector when t 11 2 Let fxyJ2yT a Evaluate f l 5 b Graph the domain of f c Find the gradient of f at the point 1 5 d Find the rate of change at the point 1 5 in the direction of v lt1 2 e In what direction will the rate of change of f at l 5 be zero f In what direction will the rate of change of f at l 5 be the greatest g Find an equation of the plane tangent to the surface z 42 y x2 0 at the point 1 5 3 h Find the linearization of fx y y x2 at the point 1 5 3 i Use the linearization to estimate f 12 49 j Find the parametric equations for the line normal to the surface at the point 1 5 3 k Suppose x 3t2 5n and y t3 uz Use the chain rule to nd and u 2 3 Show that the limit lim does NOT exist ny 00 x y 4 Find the relative extreme values for fxy 3x3 y2 9x 4y D fmfvy fw2 Let fxy x21 nd LOW J xy fuxy fyyxy fwx y Use the method of Lagrange multipliers to optimize f x y z x 2 y z 4 subject to the constraint x2 y2 z2 6 3 4 Cons1der the iterated integral J L x 2 y dydx a Estimate the value of the integral using 4 rectangles of the same size with midpoints as sample points b Evaluate the integral Math 22 Review 153 163 1 7 Let R be the planar region bounded by y x y 2x amp x 2 Evaluate 3di R Let R be the planar region outside of x2 y2 l and inside of x l2 y2 1 Find the volume ofthe solid above R and below the graph of fx y lxz y2 4 2 2 2 0 Evaluate a JD m equot dxdy b L 43062 y232dydx Let R be the planar region bounded by y 2 y sin x x 0 and x Ir Suppose that the density at any point on R equals the distance from that point to the yaXis a Find the mass of R b Find the center of mass c SET up the integral that could be used to nd the moment of inertia of R about the y axis Let R be the solid region bounded by x 0 y 0 z l amp 2x 2y z 5 Evaluate mde Let R be the solid region bounded below x2 y2 z2 4 and above 3z x2 y2 SET UP an iterated integral or integrals for yde in a cylindrical coordinates b spherical coordinates R is the region bounded by the ellipse 9x2 4y2 36 Let x 2n and y 3v a Sketch the corresponding region in the uvplane for this substitution b Use the substitution to rewrite the integral deA R Sketch the vector eld Fxy x yi x yj Suppose that the base of a fence is the portion of the cardioid r l sin 639 in the rst quadrant and the height of the fence at r 639 is 639 SET UP an integral that could be used to nd the area of the fence Let C be the graph of rt cos11ti sin11tj ntk 0 S t S 12 Evaluate the line integral J xzds C Determine if the following vector elds are conservative a Fxy2x 3yi 3x4y 8j b Fx y ex cos yi ex sinyj Let C be the straight path from 11 0 to l 21 Find the work done by Fxy lny 2xy3i 3x2y2 xyj along C Show that the line integral Cl ye dxequot dy is independent of path
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