Question 19 t Let u = it and W = Span -2 1 .For what value of t is -3 the vector U orthogonal to W?

Q: Define Euler's P-function. Showing your working, compute (5), D(23) and (115).

A:

Q: 4) Find plane area inside the polar function r = 2 and outside the polar function r = sin -0) +1 in…

A:

Q: Let F: R" R" and r e R". (a) Show that if F(r*) = 0r* is a global minimizer of ||F(x)||. (b) Show by…

A:

Q: Q5) Find volume of body bounded by z = x – y from below and z = x + y from Above inside y = x2 ,y =…

A: Volume bounded by the region

Q: (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to…

A:

Q: 5. Consider the power series (25 – 1)" a Show that the series is conditionally convergent when z =0.…

A:

Q: 1 2n Consider an = tan-1 n 1. Determine if the sequence {an}n=1 converges or diverges. 2. Is the…

A:

Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where b. A = f(t)…

A:

Q: Q5) Find volume of body bounded by z = x-y from below and z = x + y from Above inside y = x2 y = 2.

A:

Q: (-1)" Given: sin x x2n+1 for x E R 2 (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A:

Q: The base of a solid is the region enclosed by the graph of y = vln x, the line x = e, and the…

A: Given,  The base of solid is the region enclosed by y=ln(x), the line x=e and the x-axis. Also…

Q: Q5) Find volume of body bounded by z =x-y from below and z = x + y from Above inside y = x²,y = 2.

A: Volume bounded by the region

Q: Consider the linear transformation T : P2 → M22 given by [4a + c 0. T(a + ba + ca?) = |" You are…

A:

Q: too (4 – x)" /n + 5 9n · 7" Consider the power series n=1 Use Limit Comparison Test to show that the…

A:

Q: Let T : P2 –→ P2 be defined by T(p(x)) = p(3x + 6) and let B = {1, x, x²}. {1, æ, b c a If [T]B = d…

A:

Q: Question 3 Use the method of undetermined coefficients to find a general solution of the…

A: To solve given question first we write the characteristic equation of given differential equation…

Q: . x(п) %3D (2)" и() + 3(-) и(п) — 4"u(-п - 1) |

A: Given step by step explanation

Q: s + 7 L' {: (s – 5)(s + 2)2 s -

A:

Q: What is the volume generated by revolving about the x axis the area bounded by the y = 2x +1, y = 0,…

A:

Q: The locations of a spider (S) and its prey (P) are shown on the box below. The pider is on the front…

A: We will place the box on xyz co ordinate system , and then find co ordinate of points S and P .…

Q: Question 2 3 Cansider the arthagonal basis B: of R 5 Let U = -64 15 If [v]B = 6|. what is the value…

A:

Q: B-8-8- 2 1 , U3 1 and W =Span{u1, U2, U3}. For 1 Let U1 U2 = 1 |2 -3 in W ? t what value of t is the…

A: Let us consider the vector space V  Spanning set of a vector space : A set of vectors that is used…

Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where b. A = f(t)…

A:

Q: 2\2 1 .5, p=1 Vp² Is the series divergent or convergent? + 8

A:

Q: Given : an + 4 ( 1.) Show that the reries converges conditionally when x - 1 ( 2.) Find the interval…

A:

Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

A:

Q: Justifying your answer, find all integers x satisfying the two simultaneous congru- ences x = 1 (mod…

A:

Q: Let B = {b1, b2} be a basis for a vector space V. Let T : V –→ V be a linear transformation with the…

A:

Q: 1 List the elements of each of the (a) The set of integers between 1 and 50 that are divisible by e…

A: We have to right the givens sets into roaster from of set notation.

Q: 1. Detailed figure showing all flowrates, initial conditions and concentrations of each tank. 2. An…

A: Let the amount of salt in tank A and tank B at time t is x  and   y. Given information is Initially,…

Q: Prove that the following limit does not exist: lim (z,9)(0,0) I-y

A: To Prove: lim(x,y)→(0,0)x+yx-y does not exists   Here, we will check the value of the limit along…

Q: QI) Evaluate the integral dy dx using polar coordinate

A:

Q: Let V = {(x, 8) | x € R}. You are given that (V, , O) is a vector space vith (1, 8) O (x2, 8) = (x1+…

A: Given V = {(x, 8) | x ∈ ℝ} is vector space with operations (V, ⊕, ⊙) such that (x1, 8) ⊕ (x2, 8) =…

Q: L{ 13/2 }

A:

Q: Question 12 9. The eigenvalues of 1 -9] are 6. and

A: Eigen values of the Matrix are

Q: Let (V, (, )) be an inner product space and let f, g be vectors in V. if || f|| = 4, ||| 5 and || f…

A:

Q: [AAN3] Find the equation of a hyperbola that has foci at (-3, 9) , (-3, – 7and vertices (-3, –4) ,…

A:

Q: In(z2) dz Is the improper integral convergent or divergent? Solve for its value.

A: So, we will solve this integral using by-parts formula Integral I = ∫-10ln(z2) dz We can write this…

Q: Question 9 Let u(x, y) be the solution of the partial differential equation —и, —и+ уu,. х>0, у> 0,…

A:

Q: Question 26 1 2 4 6 is in NulA. 3 Let A =-1 1 -1 If | 0 1 1 then the value of a is and the value of…

A:

Q: Refer to the System of Linear Equations below. 4x1- X2- X3 -D3 -2x1 +6x2 +X3 -9 -X1 +X2 +7xg =-6…

A:

Q: A. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS d³x 3. dt3 d?x -2 dx - 35 = 0 dt 4. (D³ – 4D² + 4D)y…

A: To find the solution of homogenous linear equation with constant coefficient we assume the trial…

Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Area of the surface given by the equation z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the…

Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

A:

Q: Verify if the resulting series of constant terms when x = 0 is absolutely convergent, conditionally…

A:

Q: Determine whether the improper integral converges or diverges. If converges, find the value. In (x*)…

A:

Q: Q5) Find volume of body bounded by z = x – y from below and z = x +y from Above inside y = x² ,y =…

A: Volume bounded by the region

Q: Let T : P2 → P2 be defined by T(p(x)) =p(3 +2) and let B= {1, æ, x²}. b c] d a If [T|B = e f what is…

A:

Q: А - (BUC) — | (А — В) UC (А — В) U (A — С) | О Оption 4 Оption 1 (А — В)n (A — С) (А — В — С)

A: 1. As by distributive property A - (B ∪ C) = (A - B) ∪ (A - C) Hence Answer: Option 1 (A - B) ∪ (A -…

Q: 2) Solve the D.E xdy + (2y-x+3x)dx 0

A: