Question 4 Find the exact sum of the following series Ec(-1)* cy2k / (2k+11) k=0 (Note: Write your answers as decimal numbers rounded to five decimal places, and make sure your calculator is in radian mode).
11. (6 points) Find the sum of the following series: (a) Σ 2n +1 3η n=0 ΟΙ (5) Σ n! ΠΟ
a) b) c) What is the scalar product of -i + 3j + 2k and 3i – 2j + 2k, where i, j and k are the Cartesian unit vectors? Select one: O A. 12 OB. -7 OC. 7 OD. -5 O E. 5 What is the derivative of 4.25/4? Select one: A. 9c9/4 1629/4 B. 9 C. 5x1/4 D. 4.c 1/4 O E. 16.1/4 Which of the following is the c-coordinate of a stationary point of 3x3 – 9.x2...
prove that J2(x)=sum from k=0 to infinity [ (-1)^k/2^9@k+2)*k!(k+2)! ]*x^(2k+2) is a solution of the Bessel differential equation of order 2: x^2y'' + xy' + (x^2-4)y=0 (-1)4 9- Using the ratio test, one can easily show that the series +2converges for all e R. Prove that (-1)X h(x) = E, 22k +2k!(k + 2)! 22+2 is a solution of the Bessel differential equation of order 2: In(x) is called the Bessel function of the first Remark. In general the function...
Q2-Σ Notation Review notation by investigating In this problem we will remind ourselves of 2k k O a) Consider the similar finite sum 2* k-0 Using n - 3, rewrite this expression in expanded form, and then evaluate it. b) Rewrite Expression (2) in expanded form for n-6, and then evaluate it c) Expression (2) becomes a better approximation to Expression (1) as n grows larger. To get an idea of what (1) is, evaluate (2) using n 100. Don't...
1 points Save An Find the exact sum of the following series ((-1)* (24/(2k!)) k=0 (Note: Write your answers as decimal numbers rounded to five decimal places, and make sure your calculator is in radian mode)
Show that the sequence is arithmetic. Find the comm {Cn} = {9-2n} Show that the sequence is arithmetic. d=CH-CH-1 = (9 - 2n) - ( ) (Simplify your answers.) What is the value of the common difference? What is the value of the first term? What is the value of the second term? What is the value of the third term? What is the value of the fourth term? Write out the sum. (k+7) k=1 Find the first second, and...
Exercise 1.6.4: Prove the following by induction: (a) “k - n(n+1)(2n +1) k= 1 (b) If n > 1, then 13-n is divisible by 3. (c) For n 3, we have n +4 <2". (d) For any positive integer n, one of n, n+2, and 11+ 4 must be divisible by 3. (e) For all n e N, we have 3" > 2n +1. ()/Prove that, for any x > -1 and any n e N, we have (1+x)" 21+1x.
1(2-6 2 (Time allowed: 7 minutes) 10, k(k+2) 7 2k 2 4 k-l 5n (Time allowed: 2 minutes) 11 in(n +1) n-l 1(2-6 2 (Time allowed: 7 minutes) 10, k(k+2) 7 2k 2 4 k-l 5n (Time allowed: 2 minutes) 11 in(n +1) n-l
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....