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# Calculus III MATH 2501

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This 5 page Study Guide was uploaded by Carolyn Farrell on Monday October 12, 2015. The Study Guide belongs to MATH 2501 at Gordon College taught by Staff in Fall. Since its upload, it has received 63 views. For similar materials see /class/222095/math-2501-gordon-college in Mathematics (M) at Gordon College.

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Date Created: 10/12/15

1 STUDY GUIDE FOR FINAL EXAMINATION MATH 2501 Given the parametric equations 1 2 y 212 1 a Sketch the curve and show its orientation 10 Find the slope of the curve at t 1 c Approximate the length of the curve for 1g 15 g 4 d Assume that the parametric equations give the position of an object moving in the coordinate plane as a function of time 15 Find the speed of the object at t 4 Given the pointsA 2 1 3 B 3 5 2 and C 4 1 3 in space a Find parametric equations for the line containing B and C 10 Find an equation for the plane containing A B and C c Which of these vectors is perpendicular to the plane containing A B and C A lt55 1gt B l c 1 1l D lt101o2 3 3 3 5 Identify the graph of each equation in space 2 2 x y z a 1 4 4 b x2 y2 4 c 4x2y2 4z0 d z 2 e p 2cos 2 Givenw facyz a Find a f and 63c ayax 3x2 10 Identify the graph of the level surface Where w fx y z 2 c Use the total differential to approximate 2042 1982 0982 Given 12 y2 222 4 a Find Vf 11 1 b Find Duf 111 in the direction of v 2 3 6 c Find the maximum rate of change off at 7 1 1 1 d Find the equation of the tangent plane to the surface at the point 1 1 1 e Identify the surface Givenfxy x2 y2 2x 6y 3 a Find the critical points and classify using the Second Partials Test 10 Determine the minimum and maximum off on the closed region R Whose boundary is the square With vertices at 00 40 44 and 04 Find r1 if rIt 32k r 0 0 and r0 i j Find the acceleration vector of a particle that moves along the curve C described by rt1nti j t3k 10 1 H 1 1 14 15 1 N 9quot F 3 Calculate the speed of a particle Whose position is given by rt sinti cos tj 16t2k at the pont Where t 1 Find the maximum and minimum values of fx y z 4x2 y 2 522 subject to the constraint 2x 31 42 12 x 2 0 y 2 0 1 2 Evaluate f f e 2 dy 11 by reversing the order of integration 0 22 SC 1 2 Evaluate f f 1 e 2 3 2 lg 11 by changing to polar coordinates 1 0 Find the volume of the solid bounded by the sayplane the cylinder 12 y2 9 and the paraboloid z 2x 2 ya Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate planes the plane 21 y 2 and the paraboloid z4 x2 y2 Use Green s Theorem to evaluate f y de 61y dy Where C is the path 0 from O O to 1 0 along y 0 from 1 O to 1 1 alongx 1 and from 1 1 to 0 0 along y Use Stokes Theorem to evaluate f F T 13 Where C Fxyz 31 2yi 4x 3yj z 2yk and C is the triangle Whose vertices are 1 O O O 1 O and O O 1 03 4 ANSWERS b8 c 30023407 d 16001953 8 x Z b 5x 5yz 12 c BampC a Hyperboloid of One Sheet 10 Circular cylinder c Elliptical paraboloid d Circular Cone e Sphere 8 6f x 62f 112 312 x2 yz zz3 b Sphere c 30067 a 224 10 2 c 2 dx y 22 4 a 1 3 5 is a saddle point 10 maximum is 5 at 40 minimum is 744 at 14 ij716k ii3j6tk t2 t3 10 1 H 12 13 14 15 16 5m Minimum 1 1 Maximum 144 f6 00 121 11 11 11 1 4 e 1 4lt fe1 817

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