7.) If S*f(x)dx = 22 and S, f(x)dx = -14, find the following and clearly show how you arrived at your a. Sº f(x)dx b. 838(x)dx answer
Instructions: If you require uniformly distributed random
numbers
in [0, 1], use Matlab’s built in uniform random number generator
rand. Also,
you may NOT use any Matlab built-in functions that explicitly
perform the task
asked for in the problem.
Problem 6. Let a > 0 and set f(x)for E (-00, oo). (a) Make a plot off (b) Show that f is a probability density function (Hint: -x, when r s 0, and lrlr, when r 2 0.) (c) If X...
This is a MATLAB question so please answer them with MATLAB
steps.
Let f(z) = V3z sin(#) and P(z) =r-x-1. 1. Find f(e) 2. Find the real solution(s) to Px) 0. Hint: use the roots command. 3. Find the global minimum for f(x). Hint: plot f over [0,2] 4. Solve f()P. Hint: plot f and P over [0,21. 5. Find lim,→0+ f(x). Hint: make a vector hi make a table [x + h; f(x + h)]". 6. Find '(In 2)....
Consider the variable ject to Dirichlet boundary conditions at x = 0 and x = 1, Show that if we solve this problem using the MOL to get Av then A is symmetric and negative definite. Hint Gerschgorin's theorem may be useful for this last part
Consider the variable ject to Dirichlet boundary conditions at x = 0 and x = 1, Show that if we solve this problem using the MOL to get Av then A is symmetric and...
Select the true statements about the substitution method. It utilizes the formula , f(u(x))u'(x) dx = f(u) du. It may only be used to evaluate definite integrals. It is based on the chain rule for derivatives. It is useful to solve the integral ſ 2x sin xdx. It is based on the product rule for derivatives.
QUESTION 6 Compute the Taylor series of f(x)= sin 2x at Then show for the series above that linck; f(x) = 0 for each r QUESTION 7 Let f (x) =-x + 3, x E [0, 1] and let P be a partition of [0,1] given by 1 2 n-1 Calculate L(P) and U(P) and prove using these summations that f is Riemann integrable on [0, 1]. Also evaluate o f(x)dx.
Only 1-3)
,X, be a random sample from N(u,0") and let X and S be sample 1. Let mean and sample variance, respectively. In order to show that X and S are independent, tollow the steps below. x - x -X, and show the joint pdf of ,X,,..., X 1-1) Use the change of variable technique is (n-1)s n-u) еxp f(X,x 2a 20 av2n Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(4, /n), and...
Only 1-3)
,X, be a random sample from N(u,0") and let X and S be sample 1. Let mean and sample variance, respectively. In order to show that X and S are independent, tollow the steps below. x - x -X, and show the joint pdf of ,X,,..., X 1-1) Use the change of variable technique is (n-1)s n-u) еxp f(X,x 2a 20 av2n Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(4, /n), and...
Question 6 [10 marks a) Let f(x) = x for each xe [a,b]. Show that for any number of subintervals, the global error js(x)dx-SUS J) = 0. [6] Hint: Obtain the local error first and then calculate the global error. SCS ,h) denotes approximation using the composite Simpson's Rule. b) Determine the minimum number of subintervals so that the upper bound of the (absolute) global error for the composite Simpson's Rule applied to ja?-10x”) dx is less than 10%. [41...
can someone help me solve #5 and please show work, thank
you!
5.5 EXERCISES 1-6 Evaluate the integral by making the given substitution. 1. cos 2x dx, u= 2x 2. | xe dx, u = -x x3 + 1 dx, u= x + 1 sin cos e de, u = sin e - dx, u=x4 - 5