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).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solve all this
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cf8b658-56b4-4217-a9fb-720c6099f874%2F492d63ba-46f0-4207-b49a-0f4f20392c16%2Fpt25oew_processed.jpeg&w=3840&q=75)
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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