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Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?
(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}
(b) z * = f_{s}*g_{w} - f_{w}*g_{s}
(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}
(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}?
(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}
(b) z * = f_{s}*g_{w} - f_{w}*g_{s}
(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}
(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}?
Most Upvoted Answer
Suppose that the dependent variables z and w are function of the depen...
Understanding the Problem
The problem involves two dependent variables, z and w, which are functions of x and y defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0. The condition f_x * g_w - f_w * g_x = 1 suggests that we can apply the Implicit Function Theorem to analyze the relationships between these variables.
Analysis of Options
- Option (a): z_{a} = f_{a}*g_{A} - f_{x}*g_{w}
- This expression is incorrect as it does not align with the derivatives associated with the implicit function theorem.
- Option (b): z * = f_{s}*g_{w} - f_{w}*g_{s}
- This option resembles the correct form derived from the implicit differentiation; however, it lacks specificity regarding the variables involved.
- Option (c): z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}
- This expression is also incorrect as it improperly mixes variables and derivatives.
- Option (d): z_{x} = f_{x}*g_{w} - f_{x}*g_{x}
- This option is incorrect because it fails to maintain the correct differentiation structure.
Conclusion
None of the options presented accurately express the relationship derived from the implicit function theorem for the variables z and w in the context of the functions f and g. Therefore, careful reevaluation of the terms and their relationships is necessary to derive the correct expressions.
The problem involves two dependent variables, z and w, which are functions of x and y defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0. The condition f_x * g_w - f_w * g_x = 1 suggests that we can apply the Implicit Function Theorem to analyze the relationships between these variables.
Analysis of Options
- Option (a): z_{a} = f_{a}*g_{A} - f_{x}*g_{w}
- This expression is incorrect as it does not align with the derivatives associated with the implicit function theorem.
- Option (b): z * = f_{s}*g_{w} - f_{w}*g_{s}
- This option resembles the correct form derived from the implicit differentiation; however, it lacks specificity regarding the variables involved.
- Option (c): z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}
- This expression is also incorrect as it improperly mixes variables and derivatives.
- Option (d): z_{x} = f_{x}*g_{w} - f_{x}*g_{x}
- This option is incorrect because it fails to maintain the correct differentiation structure.
Conclusion
None of the options presented accurately express the relationship derived from the implicit function theorem for the variables z and w in the context of the functions f and g. Therefore, careful reevaluation of the terms and their relationships is necessary to derive the correct expressions.
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Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}?
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Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}?.
Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}?.
Solutions for Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? in English & in Hindi are available as part of our courses for UPSC.
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Here you can find the meaning of Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? defined & explained in the simplest way possible. Besides giving the explanation of
Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}?, a detailed solution for Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? has been provided alongside types of Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? theory, EduRev gives you an
ample number of questions to practice Suppose that the dependent variables z and w are function of the dependent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 where f_{x}*g_{w} - f_{w}*g_{x} = 1 Which one of the following is correct?(a) z_{a} = f_{a}*g_{A} - f_{x}*g_{w}(b) z * = f_{s}*g_{w} - f_{w}*g_{s}(c) z_{t} = f_{x}*g_{lambda} - f_{x}*g_{x}(d) z_{x} = f_{x}*g_{w} - f_{x}*g_{x}? tests, examples and also practice UPSC tests.
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