4،5 and 6 Part BSuppose that : m = -1 and consider the function f that is defined over R – {2} byx²-3x+1f(x) =x-2Let (C) be its representative curve in an orthonormal system.1) Prove that f is strictly increasing over R- {2}2) Prove that the straight line of equation x = 2 is an asymptote to (C).3) Prove that the point I(2; 1) is the center of symmetry of (C).4) Set up the table of variations off then draw (C).5) Consider the equation: (E): x² – (2 + 3)x + 21 + 1 = 0 where A is a realparameter.Prove that (E) admits two different real roots for all 26) Let E and F be two points of (C) such that y; = YF = 1 and let G be the center ofgravity of the triangle OEF.Find the locus of the points G as A varies.

Name: 4،5 and 6 Part BSuppose that : m = -1 and consider the function f that
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Description: 4،5 and 6 Part BSuppose that : m = -1 and consider the function f that is defined over R – {2} byx²-3x+1f(x) =x-2Let (C) be its representative curve in an orthonormal system.1) Prove that f is strictly increasing over R- {2}2) Prove that the straight

Variation of any function can be observed by substituting some arbitrary value for variables and…

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4) Set up the table of variations off then draw (C). 5) Consider the equation: (E): x2 - (2 + 3)x + 22+ 1 0 where A is a real parameter. Prove that (E) admits two different real roots for all 2 6) Let E and F be two points of (C) such that yg = yF = 1 and let G be the center of gravity of the triangle OEF. Find the locus of the points G as A varies.

4) Set up the table of variations off then draw (C). 5) Consider the equation: (E): x2 - (2 + 3)x + 22+ 1 0 where A is a real parameter. Prove that (E) admits two different real roots for all 2 6) Let E and F be two points of (C) such that yg = yF = 1 and let G be the center of gravity of the triangle OEF. Find the locus of the points G as A varies.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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