1-dx the Comparison Test. 4 Given that -dx converges, how do we know that We cannot compare 00 1 x³ -0.5 1 1 x + 2 1 -dx with - dx to say that 00 -dx also converges? Explain using 1 x³ -0.5 Find another converging improper integral that you can compare with ∞ dx converges. Why? 1 x³ -0.5 dx to say that it does

Q: If G is a group and H is a subgroup of index 2 in G show that H is a normal subgroup of G.

A:

Q: Use the graphs shown in the figure below. All have the form f(x) = ab Which graph has the smallest…

A:

Q: 32. 4+ 3+ 2+ 7-6-5-4-3-2-1 1 2 3 -3- Show Transcribed Text 567 Write an equation for the function…

A: Let fx=A(x)-∞<x<-2B(x)-2<x≤2C(x)2≤x<4D(x)4<x<∞

Q: A) Let f: R² R² be defined by k 0 f( = = 0 transformation u, where k is a scalar. The k f is called…

A:

Q: Consider the integral fe‡ dx. (a) Approximate the integral by the Trapezoidal rule using n = 4. (b)…

A:

Q: 1) To decide on a new website design, the designer asks people to rank three designs that have been…

A: Answer :-

Q: 3. Ruel is the brother of Bella. Dina is the sister of Ruel. Matthew is the brother of Tanya. Tanya…

A:

Q: Show the equivalent of (2x+3y) (4x² - 6xy +9y²) + (2x − 3y)(4x² + 6xy+9y²) 16x³ for x # 0.

A:

Q: The motion of a mass-spring system with damping is governed by y" (1) + by' (1) + 64y(t) = 0; y(0) =…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A company has $7,490 available per month for advertising. Newspaper ads cost $170 each and can't run…

A:

Q: In Exercises 9, 10, 11, and 12, show that the graph is not planar. 9.

A: A graph is not planar iff it contains k5 or k3:3 as a minor

Q: (c) Let R be a finite commutative ring with identity. Prove that an ideal in R is prime if and only…

A:

Q: 5.8. Let R = C[t]. Show that S = R[x]/((x)^(x, t)²) is not flat over R.

A: please find the attached answer

Q: 2. Solve the general cubic equation x³ + ba + bx + c = 0 with the trick of Cardan's Ars Magna.

A: The general cubic equation x3+ba+bx+c=0. We have to solve this equation using Cardan's Ars Magna.

Q: Consider the wave equation Utt- c²Uxx = 0 ᏆᏆ the half-line x = [0, ∞) with boundary condition U (0,…

A:

Q: Subgroup H of a group G is a normal subgroup of G if and only if the product of t right cosets of H…

A:

Q: Apply the inverse power method to approximate, for the matrix A , the ei­genvalue that is smallest…

A: Given : A=310131013 , x0=111 , k=6 To find : smallest eigen value.

Q: 5. Determine if the statements below are True or False. If it's True, explain why. If it's False,…

A:

Q: Suppose b is changed to b' . How large relative change can this change produce in the solution to Ax…

A: The given matrix is, A=1112501-12,  and b=123. To Find: The maximum change in the solution of the…

Q: lim n4x lim n4x Calculate the following limits, or explain why they diverge. √2n²-n +3 3n + 4 n² + 1…

A: The limit of a sequence is the value the sequence approaches as the number of terms goes to…

Q: In the Fourier Series an and bn (for any n) are found by multiplying the signal by the nth harmonic…

A: Given: Fill in the blank statement about the Fourier series.We need to fill in the given statement…

Q: The sequence (x"), 0 < x < 1, is not monotone.

A:

Q: Chapter 2, exercise 10.2(a): Let H and K be subgroups of a group G. Prove that the intersection…

A:

Q: Find the partition of = {1,2,3,4,5,6} that generates the o- o- algebra

A:

Q: dier that is the centre of a group F, So prove that = > M(x) = F. and prove that if Fis finite,…

A:

Q: Use sin + cos2 = 1 to verify the following identity: (a) tan² (x) + 1 = sec²(x) (b) tan(x)sin(x)=…

A: Introduction: Anytime trigonometric functions are used in an expression or equation, trigonometric…

Q: 1. Solve the initial value problem on the real line Utt - Uzz = sin x xx U(x,0) = 0 Ut(x,0) = sin x

A:

Q: (a) On a sheet of paper, or using a calculator or other technology, graph the three indifference…

A: Please find the attached answer.

Q: Select 2 choices. The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n+29.99,…

A: If a function y=f(x) is given then y is the value of the function and x is input for the function.…

Q: - Tell whether the following sets are open: (Justify your answe (a) (3,5) U {6} (b) (-∞, 0) U (0, 1)…

A:

Q: Chapter 2, exercise 11.6: Let G be a group that contains normal subgroups of orders 3 and 5,…

A:

Q: 4. 5. 6. Solve (-5+9i)/(1-i) Solve (5-41)/(-2+6i) Solve (3+5i) - (11-9i)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Insbase lo rodmun 2.13 Prove that for any graph G, 2p/3A(G) ≤ir(G).

A: Please find the attached soltion

Q: The table represents 2054 randomly chosen people age 25 years or older in regard to educational…

A: We know that Probability= No. of favourable outcomes/                          No. of total…

Q: (a) Use the inner product (u, v) = 2u₁v, +3u₂v₂ +₂v for u=(8,0,-8) and v=(8,3,16) in R³ to find (i)…

A:

Q: 2.22 Verify the Vizing's Conjecture for G=K, K, and T = P₁

A: Please find the attached solution

Q: 5. Definition 4: Matrix WE Rnxn is said to be normal if WTW = WWT. (a) Prove that if A is a…

A:

Q: a. Given that 22³ ... 3z + 1 can be expressed in the form Ax (x²+1) + Br+ C, find the values of the…

A:

Q: 25. 0 2x+y=4 2 26. -1 у 0 y = ex 1 x

A:

Q: 53 If the probability of an event is what is the probability of the event not happening? 92 Write…

A: If A is an event and A^c denote the complement of an even then it is well known that P(A)+P(Ac)=1.…

Q: 1. Vector Space Concepts #Vectors (a) How can vectors help represent solutions to linear systems?…

A: To Explain: (a) How vectors can be represented as solutions to linear systems, how does the number…

Q: C. Write down a sequence for the number of shapes/dots in each pattern. Explain how to obtain the…

A:

Q: prove that A Sub. treelong powevr 21 L droeb to H dreelans бога b of G if and is a only ; f every…

A:

Q: Let F denote the kth number in the Fibonacci sequence. (a) Prove that F2+1 − F²? = Fk−1Fk-2 - (b)…

A:

Q: Solve the Goursat problem: = 0 Utt- c²Uxx u|x-ct=0 = x² u/x+ct=0 = x² nt: Use the formula for…

A:

Q: Show that Sn is path-connected, by constructing for any two points x, y € Sn an explicit path…

A: We shall answer first Que only asper answering guidelines. For others kindly post again by…

Q: 16! 237 (mod 17. 19)

A:

Q: 2. Using the function f(x) = 2x+cos³ (x) - sin(x) bounded by x = 4 to x = 10 Find the area using…

A: The given problem is to find the area of region bounded by given function and x=4 and x=10 using…

Q: {B].[B]} Vector w expressed in ß is w = Vector v expressed in basis a = = {[]·[3]} Answer: 133 Wa is…

A:

Q: See how th e Rayleigh quotient method ap­proximates the dominant eigenvalue more rapidly than the…

A: Given : A=310131013 , x0=111 , k=6 To find : Dominant eigen value.