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# Multivariable Calculus MATH 2730

UNT

GPA 3.52

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This 2 page Class Notes was uploaded by Leanne Hessel PhD on Sunday October 25, 2015. The Class Notes belongs to MATH 2730 at University of North Texas taught by Staff in Fall. Since its upload, it has received 34 views. For similar materials see /class/229126/math-2730-university-of-north-texas in Mathematics (M) at University of North Texas.

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Date Created: 10/25/15

Review for Test Math 2730 Fall 704 Test l covers 9l 7 94 10l and 102 Key topics from 91 the components of the vector between two points in the plane the de nition of a unit vector and how to nd a unit vector with the same direction as a given vector the formula for the length of a vector how to determine when two vectors are in the same or opposite directions or when two vectors are parallel vector addition and scalar multiplication nding tangent and normal vectors to a curve or the graph of a function at a point Key topics from 92 the de nition of and the formula for the dot product of two vectors the Law of Cosines how to determine when two vectors are perpendicular the angle between two vectorslinescurves the formula for the projection of one vector on another and how to express one vector as a sum of a vector parallel to another vector plus a vector perpendicular to the other vector Key topics from 93 o the concept of a vector valued function I39t ti ytj o derivatives of vector valued functions velocity and speed and acceleration o integrating vector valued functions o solving initial value problems for vector valued functions Key topics from 94 o the formula for the trajectory of an object moving in the plane with a launch angle of Oz radians an initial speed of 110 and initial position 0y0 o the maximum height ight time and range of the object moving in the plane as just described Key topics from 101 o vectors in R3 and the standard unit vectors i j and k 0 addition and scalar multiplication for vectors in R3 0 length and unit vectors in R3 o the distance between two points in space 0 the midpoint of the line segment between two points in space 0 the equation of a sphere with a given center and radius Key topics from 102 o the de nition of and the formula for the dot product of two vectors in R3 o the Law of Cosines o the formula for the projection of one vector on another 0 the de nition of the cross product of two vectors in R3 lu gtlt vl and the direction of u gtlt V o the determinant formula for the cross product of two vectors in R3 o the area of a the triangle formed by three points in R3

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