2.x – 7x + 8 Part B: Consider the function f that is defined on R - {2} as: /( x)= x- 2 2 1) Prove that for all x # 2, f'(x) = 2x – 3+ x-2 d lim ((x) deduce a 2) a- Calculate lim c(v agumntote to (C

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
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Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
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2x – 7x+8
Part B: Consider the function f that is defined on R - {2} as: f(x)=
х—2
2
1) Prove that for all x + 2, ƒ(x) = 2x – 3 + -,.
x-2
2) a- Calculate lim f(x) and lim f (x),deduce an asymptote to (C).
b- Prove that the straight line (d) of equation: y = 2x -3 is an asymptote to (C).
3) Prove that the point I (2;1) is the center of symmetry of (C).
2(х- 3)(х-1)
(х-2)*
4) a- Prove that: f (x) =
b- Study the sense of variations off, then set up the table of variations of f.
c- Write an equation of the tangent (T) to (C) at a point B of abscissa 4.
d-Draw (d), (T) and (C).
5) Let E be a point of (C) of abscissa (a + 3) where a + -1.
Determine a such that the tangent to (C) at the point E is perpendicular to the
1
straight line (D) : y = -x+1.
4
Transcribed Image Text:2x – 7x+8 Part B: Consider the function f that is defined on R - {2} as: f(x)= х—2 2 1) Prove that for all x + 2, ƒ(x) = 2x – 3 + -,. x-2 2) a- Calculate lim f(x) and lim f (x),deduce an asymptote to (C). b- Prove that the straight line (d) of equation: y = 2x -3 is an asymptote to (C). 3) Prove that the point I (2;1) is the center of symmetry of (C). 2(х- 3)(х-1) (х-2)* 4) a- Prove that: f (x) = b- Study the sense of variations off, then set up the table of variations of f. c- Write an equation of the tangent (T) to (C) at a point B of abscissa 4. d-Draw (d), (T) and (C). 5) Let E be a point of (C) of abscissa (a + 3) where a + -1. Determine a such that the tangent to (C) at the point E is perpendicular to the 1 straight line (D) : y = -x+1. 4
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