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1. Evaluate each of the following: Α) Στα-2) Β) Σ(1-5) 2. Set up, do not evaluate,...
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to find .后f(x)dr Problem 2. Consider the function -2, zEQ 2, O f(r) = Show that f is not Riemann integrable on 0,1 but s Reemann integrable on this interval. Problem 3. (a) Let f be a real-valued function on a, b] such thatf()0 for all c, where c E [a, b Prove that f is Riemann integrable on a, b...
2. Evaluate the following integrals. (a) [5 marks] | el cos 4xdx -1 x (b) [5 marks] / cosdx -x³+3x²-x- dr. 1dx (c) [10 marks] (п -3)(12+2) 4 (d) [5 marks]/ dx V4-5x-2x2 dx cosh x-sinh x (e) [5 marks]] (Give the final answer in terms of e.)
5. (24 points) Evaluate each of the following. Show your work. (e) $1,1x) dx (f) sin(1+1) e* cos(1 – e*) dx (€) Set (ing) dt (h) 1,2 cos(x) cos(sin(x)) dx
Problem 2. Evaluate each of the following integrals. a) In(4x) dx 1 4x+1 dx ex b) Jo c) S (5x-2)e 6x dx
5. (4pts each)Evaluate the following integrals. s sins (1) cos (1) dx a. dx b. sz * (ln(x))?
Evaluate the following integral. 1/2 7 sin ?x -dx 1 + cos x 0 1/2 7 sin 2x dx = V1 + cos x 0 Score: 0 of 1 pt 1 of 10 (0 complete) HW Score: 0%, 0 of 10 pts 8.7.1 A Question Help The integral in this exercise converges. Evaluate the integral without using a table. dx x +49 0 dx X2 +49 (Type an exact answer, using a as needed.) 0
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
Υ 7η και 7η -15 7η -1, (Α) Σ (-1)ηθη-3 R = 2 (B) Σ (-1) +1 θη+3 R = 2 (C) Σ ( -η εθη - 2 Problem #1: Find a power series representation of the following function and determine the radius of convergence. 12 f(x) 7+14 1=0 R = 71/4 n=0 2=0 (D) Σ 70 -1, R = 71/4 (E) Σ R = 71/4 4η + 2 (F) Σ Σ 7η και R = 2 χ4η - 2...
1. Evaluate each of the following indefinite integrals. 6 Idx b. S [2 cost – 5 sin t]dt x*- x -dx c. d. I cotx sec?x dx
1. Consider the following two MA (2) models: ·zt = (1-1.3B + AB*)et with σ-10.0, . x,-(1-1.75B+ .625B2)et with σ-64. (i) Evaluate the autocovariances a,k for lags k 0,1,2 for both models to verify that they have the same acf. [5 marks] (ii) However, only one of these two models is invertible. Which one? 5 marks