Uniform Convergence

Prove that if the sum from n=1 to inf gn converges uniformly then (gn) converges uniformly to 0

Numerical Analusis Problem using Matlab

Write a function to calculate the integral from a to b of f(x) dx using the composite trapezoid rule with n equal subunits. test the code on a) the integral from 0 to pi of sin(x), b) the integral from 0 to 1 of exp(x) and c) the integral from 0 to 1 of arctan(x). Provide the codes used and all the results and work.

Numerical Analusis Problem using Matlab

With the definition that pi is the area of the unit circle, explain why pi equals 8 times the integral from 0 to 1/sqrt(2) of (sqrt(1 - x^2) - x) dx. use the Romberg algorithm to approximate the integral. Provide the codes used and all the results and work.

Numerical Analysis Problem using Matlab

Evaluate the following with Simpson's scheme: 4 times the integral from 0 to 1 of 1/(1+x^2) and 8 times the integral of (sqrt(1 - x^2) - x) from 0 to 1/sqrt(2). Provide the codes used and all the results and work.

Numerical Analysis Problem using Matlab

Write a Richardson extrapolation code and test it using f(x) = sin(x), x = 1.230959415400000, h = 1, n = 10. Provide the codes used and all the results and work.

Integrable functions

Assume that fn->f uniformly on [a,b] and that each fn is integrable. Then f is integrable and lim n->inf of the integral from a to b of fn = integral from a to b of f

Confidence Intervals

A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below: 0 260 356 4 ...continues

Confidence Interval, Normality Assumption and Very Quick Rule

Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. (a) Construct a 90 percent confidence interval for the proportion of all kernels that would not po ...continues

Newton's Method

Can you please show me how to find the roots/zeroes of f(x) = 4x – tan(x) {-pi/2 < x < pi/2}

Levels of Significance and p-Values

Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard devi ...continues