Algebra Essay Example | Topics and Well Written Essays - 1000 words

Algebra - Essay Example From the graph above, it can be seen that the parabola is rotated 45 counter-clockwise from the orientation where the axis of symmetry is the x-axis. which is the equation of a parabola centered at the origin, with the x-axis as the axis of symmetry for the parabola. With 4p = 5/2, the focal point p = 5/(42 ) = 0.88 units from the vertex of the parabola. Since p is positive, the parabola opens in the positive x-direction. If B2 - 4AC > 0, the conic section equation describes a hyperbola or pair of intersecting lines. If B2 - 4AC = 0, the conic section equation describes a parabola, line, pair of parallel lines, or no graph. Rotated conic sections can also be classified by rotating the coordinate axes by an angle where cot 2 = (A - C )/ B, by using the rotation equations, and then completing the squares for x’ and y’ until the equation is in one of the following forms: Assignment: The dot product (often referred to as the inner product in a Linear Algebra text) is a useful tool in developing several important techniques of multivariable calculus. Your task is to give a detailed description of why the gradient points in the direction of the maximum increase of a function. You may restrict your essay to R3. Your essay should include: Given that a function f is differentiable at the point (x0, y0), a directional derivative Duf(x0, y0) of the function f at a point (x0, y0) in the direction of the unit vector u = is defined by The unit vector components are given by u1 = dx/ds and u2 = dy/ds, where s is the distance along a line given by points in the x-y plane directly below points in a curve C that lies within the surface z = f(x, y). For instance, at the beginning of the line, the point (x0, y0) lies in the x-y plane directly below the point Q0 lying in the curve C within the surface z = f(x, y). At a distance s (in the direction of u) along the line in the x-y plane, the point (x, y) is