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x+2 A- Let f and g be the functions defined over [0,+ [ as: f(x)=- and g(x)= 1+ ex ex 10 . Denote by (C) the representative curve of f and by (G) the representative curve of g in an orthonormal system (O; i,j). 1) a- Determine lim f(x). Deduce an asymptote to (C). 00+4-x b- Show that f'(x)=- l− xe * — e* (1+e*)² X 0 then copy and complete f'(x) f(x) +00 the adjacent table of variations of the function f. c- Draw (C). 2) a- Determine lim g(x). Calculate g(3) and g(4). x+8 b- Calculate g'(x), then set up the table of variations of the function g. 3) The two curves (C) and (G) intersect at only one point E with abscissa a. Verify that 1.72 < a <1.73. 4) Draw the curve (G) in the same system as that of (C). B-A company produces vases. The demand function and the supply function are respectively modeled as: f(p)= and g(p)= P+2 1+eP ep 10 ; where p is the unit price expressed in ten thousands LL, f(p) and g(p) expressed in thousands of vases with p = [0.5; 4]. 1) The selling price of each vase is 25 000 LL. Estimate the number of demanded vases. 2) Assume that a 1.725. Give an economical interpretation of a. 3) E(p) represents the elasticity of the demand with respect to the price p. a- Calculate E(2). Is the demand elastic for p = 2? Justify. b- Give an economical interpretation of E(2).

x+2 A- Let f and g be the functions defined over [0,+ [ as: f(x)=- and g(x)= 1+ ex ex 10 . Denote by (C) the representative curve of f and by (G) the representative curve of g in an orthonormal system (O; i,j). 1) a- Determine lim f(x). Deduce an asymptote to (C). 00+4-x b- Show that f'(x)=- l− xe * — e* (1+e*)² X 0 then copy and complete f'(x) f(x) +00 the adjacent table of variations of the function f. c- Draw (C). 2) a- Determine lim g(x). Calculate g(3) and g(4). x+8 b- Calculate g'(x), then set up the table of variations of the function g. 3) The two curves (C) and (G) intersect at only one point E with abscissa a. Verify that 1.72 < a <1.73. 4) Draw the curve (G) in the same system as that of (C). B-A company produces vases. The demand function and the supply function are respectively modeled as: f(p)= and g(p)= P+2 1+eP ep 10 ; where p is the unit price expressed in ten thousands LL, f(p) and g(p) expressed in thousands of vases with p = [0.5; 4]. 1) The selling price of each vase is 25 000 LL. Estimate the number of demanded vases. 2) Assume that a 1.725. Give an economical interpretation of a. 3) E(p) represents the elasticity of the demand with respect to the price p. a- Calculate E(2). Is the demand elastic for p = 2? Justify. b- Give an economical interpretation of E(2).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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x+2 A- Let f and g be the functions defined over [0,+ [ as: f(x)=- and g(x)= 1+ ex ex 10 . Denote by (C) the representative curve of f and by (G) the representative curve of g in an orthonormal system (O; i,j). 1) a- Determine lim f(x). Deduce an asymptote to (C). 00+4-x b- Show that f'(x)=- l− xe * — e* (1+e*)² X 0 then copy and complete f'(x) f(x) +00 the adjacent table of variations of the function f. c- Draw (C). 2) a- Determine lim g(x). Calculate g(3) and g(4). x+8 b- Calculate g'(x), then set up the table of variations of the function g. 3) The two curves (C) and (G) intersect at only one point E with abscissa a. Verify that 1.72 < a <1.73. 4) Draw the curve (G) in the same system as that of (C). B-A company produces vases. The demand function and the supply function are respectively modeled as: f(p)= and g(p)= P+2 1+eP ep 10 ; where p is the unit price expressed in ten thousands LL, f(p) and g(p) expressed in thousands of vases with p = [0.5; 4]. 1) The selling price of each vase is 25 000 LL. Estimate the number of demanded vases. 2) Assume that a 1.725. Give an economical interpretation of a. 3) E(p) represents the elasticity of the demand with respect to the price p. a- Calculate E(2). Is the demand elastic for p = 2? Justify. b- Give an economical interpretation of E(2).
Transcribed Image Text:x+2 A- Let f and g be the functions defined over [0,+ [ as: f(x)=- and g(x)= 1+ ex ex 10 . Denote by (C) the representative curve of f and by (G) the representative curve of g in an orthonormal system (O; i,j). 1) a- Determine lim f(x). Deduce an asymptote to (C). 00+4-x b- Show that f'(x)=- l− xe * — e* (1+e*)² X 0 then copy and complete f'(x) f(x) +00 the adjacent table of variations of the function f. c- Draw (C). 2) a- Determine lim g(x). Calculate g(3) and g(4). x+8 b- Calculate g'(x), then set up the table of variations of the function g. 3) The two curves (C) and (G) intersect at only one point E with abscissa a. Verify that 1.72 < a <1.73. 4) Draw the curve (G) in the same system as that of (C). B-A company produces vases. The demand function and the supply function are respectively modeled as: f(p)= and g(p)= P+2 1+eP ep 10 ; where p is the unit price expressed in ten thousands LL, f(p) and g(p) expressed in thousands of vases with p = [0.5; 4]. 1) The selling price of each vase is 25 000 LL. Estimate the number of demanded vases. 2) Assume that a 1.725. Give an economical interpretation of a. 3) E(p) represents the elasticity of the demand with respect to the price p. a- Calculate E(2). Is the demand elastic for p = 2? Justify. b- Give an economical interpretation of E(2).
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