EBK CALCULUS FOR BUSINESS, ECONOMICS, L
14th Edition
ISBN: 9780134856667
Author: Stocker
Publisher: VST
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Chapter A.4, Problem 35E
(A)
To determine
To check: Whether the solution is correct and if wrong, to explain how it can be corrected.
(B)
To determine
To find: The correct solution for the incorrect solution.
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Exercice 2:
Soit & l'ensemble des nombres réels.
Partie A
Soit g la fonction définie et dérivable sur R telle que, pour tout réel x. g(x) = - 2x ^ 3 + x ^ 2 - 1
1. a) Étudier les variations de la fonction g
b) Déterminer les limites de la fonction gen -oo et en +00.
2. Démontrer que l'équation g(x) = 0 admet une unique solution dans R, notée a, et que a appartient à | - 1 ;0|.
3. En déduire le signe de g sur R.
Partie B
Soit ƒ la fonction définie et dérivable sur R telle que, pour tout réel s. f(x) = (1 + x + x ^ 2 + x ^ 3) * e ^ (- 2x + 1) On note f la fonction dérivée de la fonction ƒ sur R.
1. Démontrer que lim x -> ∞ f(x) = - ∞
2. a) Démontrer que, pour tout x > 1
1 < x < x ^ 2 < x ^ 3
b) En déduire que, pour x > 1
0 < f(x) < 4x ^ 3 * e ^ (- 2x + 1)
c) On admet que, pour tout entier naturel n. lim x -> ∞ x ^ n * e ^ (- x) = 0 Vérifier que, pour tout réel x, 4x ^ 3 * e ^ (- 2x + 1) = e/2 * (2x) ^ 3 * e ^ (-2x) puis montrer que: lim x -> ∞ 4x ^ 3 * e…
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Chapter A.4 Solutions
EBK CALCULUS FOR BUSINESS, ECONOMICS, L
Ch. A.4 - Reduce each fraction to lowest terms....Ch. A.4 - Reduce each rational expression to lowest terms....Ch. A.4 - Prob. 3MPCh. A.4 - Combine into a single fraction and reduce to...Ch. A.4 - Express as a simple fraction reduced to lowest...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 3ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 5E
Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 7ECh. A.4 - Prob. 8ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 14ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 18ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 25ECh. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 30ECh. A.4 - Prob. 31ECh. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 34ECh. A.4 - Prob. 35ECh. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - Prob. 37ECh. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...
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