# chebyshev

1. ### Understanding a specific Chebyshev integral

I have a situation where I'm trying to understand the physics of a cooling tower. Part of the solution for the model I'm working with involves an integral: C = \int_{T_{low}}^{T_{high}} \frac{1}{\left(h' - h_a\right)} dT where h' is a slowly varying, monotonically increasing function with...
2. ### Chebyshev's Theorem

I have this problem: "In a distribution of 160 values with a mean of 72, at least 120 fall within the interval 67â€“77. Approximately what percentage of values should fall in the interval 62â€“82? Use Chebyshevâ€™s theorem." If I knew what the standard deviation was, I would know how to do...
3. ### Gauss Chebyshev formula

Use Gauss Chebyshev formula with $n=3$ to approximate the value of the integral. $$\int \frac{x^4}{\sqrt{1-x^2}}dx$$ from -1 to 1. Also compare the result with true value, where the zeros and the corresponding weights of the following simple set of orthogonal polynomial is given as below...
4. ### Chebyshev's inequality

We`re throwing symetric cube for 720 times. Using Chebyshev's inequality show that the probability of throwed 4 is in the interval (100,140) How can i solve this one?
5. ### Chebyshev polynomials

These problems are about a useful class of polynomial called Chebyshev polynomials which are defined as: T_n(x)=cos(n cos^-^1x) (a) what are the domain(s) and range(s) of the functions? (b) give equivalent polynomial definitions for T_n(x) when n=0,1,2,3. That is show that the definition...
6. ### Euclidean vs Manhattan vs Chebyshev distance?

Imagine three points A,B and C. Is it possible AB>AC in Euclidean distance but AC>AB in Manhattan or Chebyshev distance? Or if AB>AC in one distance norm then AB>AC in any other distance norm? I will be grateful if you state your source(s). Thanks from Greece Pericles
7. ### Chebyshev's theorem

1. In a certain distribution, the mean is 50 with a standard deviation of 6. Use Chebyshev's theorem to tell the probability that a number lies in the following interval. Round your results to the nearest whole percent. Less than 26 or more than 74
8. ### Chebyshev's theorem

Could anyone please kindly explain what this Chebyshev Theorem really tries to convey and its practical use ?? I am not getting it clearly its use and significance.. Thank you
9. ### Chebyshev polynomials / Odd Eigenvalues (12/04/06)

The following proof was given for the problem on Chebyshev polynomials: "Let z = e^(ix), and y = 2 cos(x) Then (z^n) is a polynomial in cos(x) and sin(x), say A( cos(x), sin(x) ) whose real part is cos (nx), but Re{A( cos(x), sin(x) ) contains only even powers of sin (x). Replacing...