Q2.4 2 Points U-substitution undoes the product rule O True O False Q3 12 Points Find...
(3 points) Consider the indefinite integral X – 3 (3x - 2)2 dx. The substitution u = 3x – 2 transforms the integral into: | du (This answer must be a function of u.) Note: You are not asked to evaluate the integral.
In Problems 14-18, evaluate the given definite or indefinite integral, using u-substitution if appropriate. (12 points each) x + 3x -4 dx r? 14. 15. S (x+12 +2x - 3)dx
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.
Description -12 POINTS LARCALCET7 8.4.003. Find the indefinite integral using the substitution x = 2 sin(e). (Use C for the constant of integration.) ya - 1233/2 ox Show My Work (Required) What steps or reasoning did you use? Your work counts towards your score. You can submit show my work an unlimited number of times.
5.1 Let U a in f(X;0) ae then E(U)=0. O TRUE O FALSE 5.2 Let X1, ..., X. * N (14.0). If o’ is unknown and we want to derive a confidence interval for the true population mean, then distribution of the appropriate pivotal quantity is Chi-Square with n degrees of freedom. O TRUE O FALSE Q5.3 1 Point 5.3 Let X.....X.1080). Assume both i and o? are unknown. Then the MLE of a' is unbiased, O TRUE O FALSE...
State whether the following statements are true or false as x→00 (c)x-O(x+6) (g) In x-o(in 2x) (a) x- o(3x) (d) x = 0(2x) (h) yx2 + 6 =0(x) (e) e x = o(e4x) (f) 3x + Inx=0(x) (a) Is x = 0(3x) as x→ oo true or false? O False O True b) Is x = 0(x + 6) as x→ oo true or false? False O True (c) Is x-O(x + 6) as x-> oo true or false? O...
Find f'(x) and simplify. f(x)=xinx Which of the following shows the correct application of the product rule? X O A. (x) (3x?) +(In x) 08 (1) () + (1x) (3x? OC () (1) - (Inx)(3x) op (1J ) (227) ho
2. Mark each statement True or False. Justify your answer. (6 points each) (a) (A\B) U ( BA) = (AUB) (ANB). (m) º (7.1+5) = (a :) n=2 1 3. Let A = {J,Q,K) and B = {4,0}. Find (list thc clements of) the set A x B. Find |A x B) and P(A x B) (9 points) 3
Q1 Existence 5 Points Every square matrix has at least one eigenvalue. O True O False Save Answer Q2 Basis 5 Points Let A be an (n xn) matrix, and assume that A has n different eigenvalues, then there is a basis of R" consisting eigenvectors of A. O False O True Q3 Computation 5 Points [ 1 Find the algebraic and geometric multiplicity of the unique eigenvalue of 1 1 Write your answer in the form [a, g] where...
(a) i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0) Make the substitution u=2x^2−4x+2, and write the integrand as a function of u, ∫(4x−4)(2x^2−4x+2)^4 dx =∫ and hence solve the integral as a function of u, and then find the exact value of the definite integral. ii) Make the substitution u=e^(3x)/6, and write the integrand as a function of u. ∫ e^(3x)dx/36+e^(6x)=∫ Hence solve the integral as a function of u, including a constant of integration c, and then write...