clc;
clear all;
y=linspace(0,3,100); %y is input
z=zeros(1,100);
syms x;
%a)
fun= x*exp(-(x^2));
for i=1:100
C= int(fun,0,y(i));
z(i)=vpa(C);
end
% z is exact value
%b) zero order approximation (zoa)
zoa=mean(z);
%c) first order approximation (foa)
P=polyfit(y,z,1);
%P(1) is slope and P(2) is constant term:::P(1)x+P(2)
%d) plot
plot(y,z,'ro');
hold on;
plot(y,z);
if you have any doubt please write it in comment box
USE MATLAB Problem 3. Consider the running integral 'dx 0s xs3 Determine: (a) the exact value...
Problem 3. Consider the running integral T dx 0x3 0 Determine: (a) the exact value over the domain, (b) the zero-order approximation, and c) the zero-order approximation. Apply 100 points on the interval 0xs3. (d) Plot the approximation as a continuous curve and the exact value as a sequence of o's Q8. What is exact value of z for 0<x<3 ? Q9. What is approximate value of z for 0sx<3 when using zero-order approximation with 100 points over domain? Q10....
Consider the integral 8. eT dx Use Simpson's Rule with n = 6 to estimate the value of the integral. (a) (b) Your friend chose instead to estimate the integral above using the Midpoint Rule with n = 6, Noting that the second derivative: 4x2-4r +3)e z5/2 is an increasing function over the interval [1, 4], determine the maximum possible error in your friend's estimate Consider the integral 8. eT dx Use Simpson's Rule with n = 6 to estimate...
10. Let and consider approximating its average value on the interval (0,2) given by the integral 4-2 dx. 0 (a) Use Calculus to show that the the exact answer is π/2. (Hint: You may want to substitute 2 sin , and later use the trignometric identify cos(20)-1-2 cos2 θ). (b) Assume r is uniformly distributed in (0,2). What is the expected value, E f ()] How is the formula for expected value related to the expression given by expression in...
Sec6.5: Problem 6 Previous Problem List Next (2 points) Book Problem 17 4, to approximate the integral 7e dx (a) Use the Midpoint Rule, with n MA (Round your answers to six decimal places.) (b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI-89. 7edx (c) The error involved in the approximation of part (a) is Ем — Те ах Ма (d) The...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Find the approximate values of 1 when the step size h-: 2 and h 1 , respectively. (b) Find an upper bound of the step size h in order to guarantee that the absolute error (in absolute value) of the estimate is less than 0.001. Hint: 2 sin x cos x = sin (2x). I cos x I " The arguments of all trigonometric...
462 1.231251937 4 Yy-2(3)(1.061616 237712 4. Given the initial value problem and exact solution: a) Verify the solution by the method of Undetermined Coefficients. x-y+2 y(0)4 ()3e +x+1 (10 points) b) Apply the Runge-Kutta method to approximate the solution on the interval [0.0.5] with step size [15 points h = 0.25 . Construct a table showing six-decimal-place values of the approximate solution and actual solution at each step
1. Complete the table below for f(x)=3". Use exact values. No work needed. [1.25 points) - 101 y = f(x) 2. Consider the functions gtx)=(13)" and h(x) =--() +4 12.5,1.25, 1.5 points) a) The points given below (in the first column) belong to g(x)= - Perform two b) Use the point found in part a) to sketch a graph of y=h(x). Include the horizontal asymptote as a dashed line. Approximate point placement where necessary. transformations (and show how the points...
IN PYTHON 3: In this version of Radix Sort we use Queues very naturally. Let us consider the following set of positive integers: 311, 96, 495, 137, 158, 84, 145, 63 We will sort these numbers with three passes. The number of passes is dependent on the number of digits of the largest number - in this case it is 495. In the first pass we will go through and sort the numbers according to the digits in the units...
Consider the initial value problem y' +y=e-, with y(0) = 0. PROJECT 1.) Find the exact solution to this equation, say 0(x). 2.) Use MATLAB to plot 6(x) in the interval [0.0, 4.0] . Use sufficient points to obtain a smooth curve. 3.) Now create a MATLAB program that uses Euler's Method to approximate the values of $(2) at N = 10 equally spaced points in (0,4). Plot these points on the same plot that was generated in part 2....