Equivalent Trigonometric Expressions - University of …
In This Module Definition of an Identity A mathematical identity is an equation or statement that is true for all permissible values of the variables in
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Even and Odd Polynomial Functions - University of Waterloo
courseware.cemc.uwaterloo.caare neither even nor odd. Along with an odd degree term x3, these functions also have terms of even degree; that is an x2 term and/or a constant term of degree 0. It appears an odd polynomial must have only odd degree terms. Symmetry in Polynomials Consider the following cubic functions and their graphs. 21 — 3 x3 — 21 —213 2r2
Sigma Notation and Riemann Sums - University of Waterloo
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The Scalar Equation of a Plane - University of Waterloo
courseware.cemc.uwaterloo.caExamples Example 3 Find the distance from the point Q (1, 4, 7) to the plane containing the points X (0, 4, Solution —1), Y (6, 2, 5), and First, determine the scalar equation of the plane by using the three points to generate two vectors, dl and d2 , followed
Equations, Panels, Three, Sacral, The scalar equation of a plane
The Intersection of Three Planes - University of Waterloo
courseware.cemc.uwaterloo.caFind all points of intersection of the following three planes: x + 2y — 4z = 4x — 3y — z — Solution Substitute y = 4, z = 2 into any of (1) , (2), or (3) to solve for x. Choosing (1), we get x + 2y — 4z — 3 + 2(4) — 4(2) 3 3 Therefore, the solution to …
Panels, Three, Intersection, The intersection of three planes
The Intersection of Two Planes - University of Waterloo
courseware.cemc.uwaterloo.caWe have shown that the two planes are parallel and have a point in common, so the planes are in fact coincident The solution is the set of all points in either plane Note: If P2 (5, —1, 0) did not lie on m, the planes would have been parallel and distinct In this case, there would be no intersection between the two planes. Examples Example 1
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Characteristics of Polynomial Functions
courseware.cemc.uwaterloo.cathe fourth quadrant. Cubic Functions: y = ax-3 + bx2 + cx + d, a 0 It is possible for the graph of a cubic function to have 1, 2, or 3 x-intercepts depending on whether the graph has a turning point and the position of the graph on the axis.
Functions, Characteristics, Fourth, Turning, Polynomials, Characteristics of polynomial functions
Transformations of the Sine and Cosine Functions
courseware.cemc.uwaterloo.caTransformational Form The Sine Function y = asin[b(x — h)] k The Cosine Function y = acos[b(x — h)] + k cas — cos Let's review the role of the parameters a, b, h, and k …
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Finite Differences Of Polynomial Functions
courseware.cemc.uwaterloo.caFinite differences provide a means for identifying polynomial functions from a table of values. Knowing the relationship between the value of the constant difference and the leading coefficient of the function can also be useful. Example 2
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