Midterm 1 Study Guide
Midterm 1 Study Guide Math 2419
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This 11 page Study Guide was uploaded by Saul Cervantes on Tuesday September 29, 2015. The Study Guide belongs to Math 2419 at University of Texas at Dallas taught by Anotoly Ezlydon in Fall 2015. Since its upload, it has received 227 views. For similar materials see Accelerated Calculus II in Mathematics (M) at University of Texas at Dallas.
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Date Created: 09/29/15
CALCULUS II MIDTERM 1 STUDY GUIDE Equations to know Distance between two points x1 x22 y1 yZ2 21 222 Standard Equation of Sphere X a2 y b2 z c2 R2 Dot Product Formula uV uVcosa Cross Product Formula 139 j k uXvdetu1 uZ u3detu2 u3iu1 u3ju1 uzk v1 v2 v3 v2 v3 v1 v3 v1 v2 uv IIvIIZ Projection of u onto V projVu Parametric equation of a line Lt tltu1 u2 u3gt A Standard Equation of Plane ax by cz d O Surface Area SA f 21tfx 1 f x2 dx Where fX is a given function Parametric Form of Surface Area SA 21131 ff x 2 y392 dx Arc Length ff f62 f 62d6 Area iffdeH Tlt vt Ilr t 39 vt Tangent Vector Tt Normal Vector Given Tt ltX ygt then Nt lt y Xgt TIt Nt 39 lT t d Tangential acceleration aT a I vt I I 2 Normal acceleration aN I at IaTIZ IIT t Ilr39xxrxll Ilr tll r t3 Given fX y then Kt If x 32 1f39x Curvature Kt Concepts 39 If rt is a position vector then velocity vt r t and acceleration at r t v t and speed vt A curve is a smooth if and only if X and y are both continuous and not zero at the same time A unit vector is any vector of length 1 Sphere A set of all points equidistant from a given point where the given point is the center and the distance between center and all other points is the radius Two vectors are parallel if ltul u2 u3gt ltcvl cv2 cv3gt for some scalar c Orthogonal is the same as perpendicular Two non zero vectors are perpendicular orthogonal if and only if uv O A matrix is a rectangular array of numbers When checking if two lines intersect first set them equal to each other and solve If there is a solution the lines do intersect Two planes are parallel if their normal vectors are parallel Given equation of plane aXXO by y0 cz z0 0 then the normal vector n lta b cgt a point lying on the plane is A X0 yo ZQ A graph of every function is a curve but not every curve is the graph of a function If the second derivative of a function is greater than zero the function is concave up If the second derivative of a function is less than zero the function is concave down Rectangular vs Polar Rectangular Polar A X y A r 0 X rcosO r X2 y2 y rsinO 0 tan391 g Example Problems w W7 012ja22 he mng Mm z a JmMmm cm NLQS Xaoaw w The following two images are one single problem
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