real analysisuse method in example 35.2 to solve a b c d Example 35.2. Let f(x) = x² and consider the closed interval [3, 7].Let P be the partition (3, 3.2, 5.1, 6, 6.8, 7) (so n = 5 here). Notethat ||P|| = 1.9.Let S be the sampling points (3.15, 4, 5.5, 6, 7). ThenRS(f,P,S) = 3.15°(.2)+4²(1.9)+5.5°(.9)+6°(.8)+7°(.2) = 98.2095 (exactly).This number approximates the area under y = x², above the T-axis,between a = 3 and x = 7. Of course, fromn calculus we know that theactual value of this area is f x² dx =7333* = 105.3.33We can now define f(x) dx. Loosely speaking, it is the number Iso that if we consider partitions P of very small norm, then RS(f, P,S)is very close to I for all S. Such a number need not exist, however,and so f(x) dx is sometimes undefined.SO (1) Let f(x) = x defined on the closed interval [0, 4].(a) For the partition P =RS(f,P,S) = 8.(b) For the partition P =RS(f,P,S) = 9.(c) For the partition P =sampling point S for P so that RS(f,P,S)(d) Describe a partition P =(0, 1, 2, 3, 4) of [0, 4], find a list of sampling points S =($1, 82, 83, 84) for P such that(0, 1, 2,3, 4) of [0, 4], find a list of sampling points S = (s1, $2, $3, 84) for P such that(0, 4) of [0, 4] and any real number y such that 0 < y < 8, show that there is a list of= y. (Note that the list S will have just one member.)(x0, x1,..., x100) of [0,4] and a list of sampling points S for P such that RS(f,P,S) <0.01.

Given fx=x. Answer for sub question a: Given, P=0,1,2,3,4 a partition of 0,4. To find a list of…

Let f(x) = x defined on the closed interval [0, 4]. (a) For the partition P = RS(f,P,S) = 8. (b) For the partition P = RS(f,P,S) = 9. (c) For the partition P = sampling point S for P so that RS(f,P,S) (d) Describe a partition P = (xo, x1,..., x100) of [0, 4] and a list of sampling points S for P such that RS(f,P, S) < 0.01. (0, 1, 2, 3, 4) of [0, 4], find a list of sampling points S ($1, 82, 83, 84) for P such that (0, 1, 2, 3, 4) of [0, 4], find a list of sampling points S = (81, 82, 83, 84) for P such that (0,4) of [0, 4] and any real number y such that 0 < y < 8, show that there is a list of = y. (Note that the list S will have just one member.)

Let f(x) = x defined on the closed interval [0, 4]. (a) For the partition P = RS(f,P,S) = 8. (b) For the partition P = RS(f,P,S) = 9. (c) For the partition P = sampling point S for P so that RS(f,P,S) (d) Describe a partition P = (xo, x1,..., x100) of [0, 4] and a list of sampling points S for P such that RS(f,P, S) < 0.01. (0, 1, 2, 3, 4) of [0, 4], find a list of sampling points S ($1, 82, 83, 84) for P such that (0, 1, 2, 3, 4) of [0, 4], find a list of sampling points S = (81, 82, 83, 84) for P such that (0,4) of [0, 4] and any real number y such that 0 < y < 8, show that there is a list of = y. (Note that the list S will have just one member.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Show that the random process X(t) =cos(2π fot + θ) Where θ is an random variable uniformly distributed in the range {0, π/2, π, π/3} is a wide sense stationary process .
IF F(x, y) is the value of the joint distribution function of X and Y at (x, y), show that the marginal distribution function of X is given by G(x) = F(x, ∞) for - ∞ <x < ∞ Use this result to find the marginal distribution function of X for the random variable F(x, y) = { (1-e-x2 ) (1- e-y2) for x>0, y> 0 and 0 elsewhere
Let (X, Y ) be independent and uniformly distributed random variables (RVs) on the interval[0, 1]. Equivalently, let (X, Y ) be a point chosen uniformly at random in the unit box [0, 1] × [0, 1] on the(x, y) plane. Define the RV Z ≜ √X^2−Y^2 as the random distance of the point (X, Y ) from the origin (0, 0). Find the cumulative distribution function (CDF) for the RV Z.
Find and classify all the critical points of f(x,y) = x3+3x2-3x-y3+6y2-9y. Find the maximum and minimum of f on the region x[-1,1], y[-1,1]
Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?
Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?
Find the critical region/s using z-table a) a = 0.015, two-tailed test b) a = 0.025, left-tailed test c) a = 0.0125, right-tailed test
Let X and Y be continuous random variables with joint distribution function, F (x,y). Let g (X,Y) and h (X,Y) be functions of X and Y. PROVE Cov (X,Y) = E[XY] - E[X] E[Y]
Let X1,...,Xn be a random sample from the distribution f(x) = 2x, 0 < x < 1. Find the distribution of the sample maximum X(n)
Let X 1 ,X 2 ,...,X n be a r.s. of size n from a distribution N(theta, 1) find best critical region of size a for testing H 0 : theta=0 against H 1 : theta=1 , also find the value of c if n = 25 and a = 5%.
Suppose X has uniform distribution on (−1, 1) and, given X = x, Y is uniformly distributed on (−(1-x^2)^1/2, (1+x^2)^1/2). Find the join denisty of X and Y.
Identify the locations of transition points on the interval [-pi,pi] for f(x)=2sin(x)+x.