Suppose the following data points are generated by a smooth function f(x):X-1-2/3-1/30 1/32/31f(x) 0.8415 0.4300 0.1109 0 0.1109 0.43000.8415Approximate f f(x) dx using the composite Simpson's rule with n = 6 subintervals.0.47250.47670.61850.6204Use Romberg integration to find an 0(h) approximation of f 4sin(x²) dx.1.22071.2398O 1.24101.6829

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In economics the Lorenz curve is a function L(x) defined on the interval [0, 1] as follows. The x-axis is the proportion of people in a country’s population ordered from poorest to richest, e.g. x = 0.4 is the poorest 40% of the population, x = 0.9 is the poorest 90% – so all except the richest 10%. The y-axis measures the proportion of total income earned in the country.A point y = L(x) is on the Lorenz curve if the poorest 100x% of the population earn 100y% of the income. For example if L(0.6) = 0.35 then the poorest 60% of the population earn only 35% of the income in the country. It is always true that L(0) = 0 and L(1) = 1.If income is spread equally across the country, then L(x) is the straight line y = x. In such a country everybody earns the same. In reality the Lorenz curve is concave up and lies below the line y = x for all countries. The shaded area between y = L(x) and y = x measures how far income distribution is from being equal.The Gini coefficient for a country is…
Consider the following function. f(10) 5, f'(10) = -0.7; x 10.2 (a) Write a linearization forf with respect to x fL(x) (b) Use the linearization to estimate f at the given input (10.2)
The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf. - (x - 3)2 2s x5 4 f(x) = - otherwise (a) Sketch the graph of f(x). f(x) f(x) 1.0| 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 X 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 f(x) f(x) 1.0 1.0f 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 (b) Find the value of k. (c) What is the probability that the actual tracking weight is greater than the prescribed weight? (d) What is the probability that the actual weight is within 0.15 g of the prescribed weight? (Round your answer to four decimal places.) (e) What is the probability that the actual weight differs from the prescribed weight by more than 0.45 g? (Round your answer to four decimal places.)
Suppose the following data points are generated by a smooth function f(x): 0.0 0.5 1.0 1.5 2.0 2.5 3.0 f(x) 2.1111 2.4484 2.5708 2.4484 2.1111 1.6415 1.1546 Approximate S() dx using the trapezoidal rule with 3 sub-intervals. 2.5793 2.6125 6.3148 5.5878
DETERMINE IF THE FOLLOWING FUNCTIONS ARE CONTINUOUS ON THE INTERVAL I. PLEASE ANSWER THE SUBPARTS A-E

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Suppose the following data points are generated by a smooth function f(x): X -2/3 -1/3 0 1/3 2/3 1 f(x) 0.8415 0.4300 0.1109 0 0.1109 0.4300 0.8415 Approximate f(x) dx using the composite Simpson's rule with n = 6 subintervals. 0.4725 0.4767 0.6185 0.6204