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Find C of Cauchy’s mean value theorem for the function 1/x and 1/x2 in [4, 6]
- a)4.8
- b)5
- c)Does not exist as 1/x is not continuous
- d)Does not exist as 1/x2 is not differentiable
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Find C of Cauchy’s mean value theorem for the function 1/x and 1...
f(x) and g(x) are continuous in [4, 6]
f(x) and g(x) are differentiable in [4, 6]
g′(x) = −2 / x3
g’(x) ≠ 0 in (4, 6)
Now, according to Cauchy’s mean value theorem
∴ c = 4.8
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Find C of Cauchy’s mean value theorem for the function 1/x and 1...
In mathematics, the Cauchy constant, denoted as C, is a constant that appears in the Cauchy distribution, a continuous probability distribution named after the French mathematician Augustin-Louis Cauchy.
The Cauchy distribution has a probability density function given by f(x) = (1/πC) * (C^2 / (x^2 + C^2)), where x is a real number and C > 0 is the Cauchy constant.
The value of C determines the shape and spread of the Cauchy distribution. A larger value of C leads to a wider and less concentrated distribution, whereas a smaller value of C leads to a narrower and more concentrated distribution.
The Cauchy constant C can be chosen based on the specific application or problem being studied. It is typically chosen to match the desired spread or concentration of the distribution for the given context.
The Cauchy distribution has a probability density function given by f(x) = (1/πC) * (C^2 / (x^2 + C^2)), where x is a real number and C > 0 is the Cauchy constant.
The value of C determines the shape and spread of the Cauchy distribution. A larger value of C leads to a wider and less concentrated distribution, whereas a smaller value of C leads to a narrower and more concentrated distribution.
The Cauchy constant C can be chosen based on the specific application or problem being studied. It is typically chosen to match the desired spread or concentration of the distribution for the given context.
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Find C of Cauchy’s mean value theorem for the function 1/x and 1/x2 in [4, 6]a)4.8b)5c)Does not exist as 1/x is not continuousd)Does not exist as 1/x2 is not differentiableCorrect answer is option 'A'. Can you explain this answer?
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