Use Green's theorem to find the area integral if V(x.y) = (x²+y®)į+ (x²=y®\j¸ where C is a solid region bounded by (-1,0), (1,0) and the parabola y = 2–x² and anticlockwise orientation. Note: Solve the problem using rectangular coordinates. 1. 1 1.7 1.4 1.5 1.4 1.3 1.과 1.1 08 04 04 02 04 06

Q: Solve this ODE using the Frobenius Method x*y"+x°y'_2y = 0

A: In the Frobenius method we will start by assume a solution of the form  y=xk∑n=0∞anxn

Q: what Is the conjugate of Js -J2i ? a. Jo -Joi d. -i b.Ja -ぶ

A:

Q: f(t) = t sinh 5t 5s 5s С. (s2+25)2 А. (s2-25)2 10s 10s В. (s2-25)2 D.- (s2+25)2

A:

Q: Use Green's theorem to find the counter-clockwise circulation for the field V = 2xyi – 3x°yj, where…

A:

Q: Ax) = Ln=0 n! e Show that: GAx)dx = En=1 n(n+1) (–2)"-1 (n +2)! ||

A: Here we use integration and series theorems to find the solution.

Q: Suppose that 0 <c <n/2. For what value of c is the area of the region enclosed by the curves y=cosx,…

A: Suppose that 0 &lt; c &lt; π2. We have to find the value of c at which the area of the region…

Q: Find the truth table for the given statements (a) (p ∨ r) ∧ (q ∨ r) (b) p ∨ (∼p → q) (c) (p →…

A:

Q: Assuming a matrix A is row equivalent to /, and it takes 4 elementary row operations to convert A to…

A: Given matrix, A=01412-1580 To find: a) Reduced Matrix  using row elimination transformation…

Q: Solve the given LP problem using the Simplex Method Minimize: Z = 25x1 + 35x2 Subject to: 3x1 + 4x2…

A: The given problem is to solve the given linear programming problem using the simplex method with…

Q: For integers æ, y, notation æ|y means that x is a divisor of y. (For example 5|30, but it is not…

A: After the assumption that 3| (22k - 1), we need to mathematically formulate this.  i.e., from the…

Q: 2. Determine a basis for and the dimension of the solution space of the homogeneous system X3 + X4 +…

A:

Q: Suppose that the marginal propensity to save is ds = 0.3 – dy (in billions of dollars) V 9y + 6 and…

A:

Q: 4. Determine which of the following sets of n x n ma- trices are subspaces of Mnxn (R). a) The n x n…

A:

Q: Consider the sequence {a„} where a, is given by (n³ – 1)/nº, (n² + 1)/n², if n is even. if n is odd,…

A: The given question is related with  sequence. Consider the sequence an , where an is given by…

Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

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

Q: Calculate Vf when f 3x z-y7+ 4x'y+ 2x - 3y-5 at the point (1, 1, 0).

A:

Q: -2 -2 B= 3 4 If A= 2 3 then (4+B) is: -1 1 (a) 1 (b) does not exist (c) is a skew-symmetric (d) none…

A:

Q: f(t) = te3t cosh 4t s²-6s+7 s2-6s-7 А. (s2-6s+25)2 С. C. (s2-6s-25)2 s2-6s+25 В. (s2-6s-7)2 s2…

A:

Q: (3) A firms production function is Q(L) = 15L -0.1Ľ , where output (Q) is a function of a single…

A:

Q: Find a primitive root (i.e. a primitive (p? – 1)st root of unity) in F3[i], and write down the…

A: F3i : It is the unique field of three elements. It can be defined as the ring of integers of modulo…

Q: where P =n+p+h is the total population, and a and b are some real numbers (which you do not need to…

A: We are given the following information. The population has been divided into three categories:…

Q: NUMERICAL ANALYSIS

A: Based on image we shall solve all the questions, When n=2, the problem becomes: Given: X0X1 fo f1…

Q: Find the solution. (D² - 20 - 3)y = 0; when x = 0, y = 0, y'= 4 A y = e-e B y =e+e y = e y = -e

A:

Q: Find the surface area of a cylinder with a base radius of 2 m and a height of 5 m. Write your answer…

A: Given:A cylinder with a base radius of 2 m and a height of 5 m

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

A:

Q: In Exercises 1-7, (X,M) is a measurable space. 1. Let f : X R and Y = f-1(R). Then f is measurable…

A: Given: Let's consider X,M is a measurable space.  Here f:X→ℝ¯ and Y=f-1ℝ

Q: Provide an appropriate response. How do you 13) Let f have a derivative on an interval I. f has…

A: Given : f have a derivative on an interval I. And f' has a successive distinct zeros at x = 1 and…

Q: Find the surface area of a cylinder with a base diameter of 12 in and a height of 9 in. Write your…

A: To find the surface area of cylinder.

Q: FALSE and give a counterexample and justify or explain briefly why this is such. (a) Let A and B be…

A: Here we use examples and theorems for sequences.

Q: Match the theorem or rule for what it justi 25 One pair of consecutive sides are congruent It has…

A: Given: One pair of consecutive sides are congruent:  It has been proven to be a mombus and a…

Q: Problem: A loan of Php 1500 at 12 % annual interest rate. The loan was made on June 22 and due on…

A:

Q: (D5 + D4 - 7D3 - 11D2 - 8D - 12)y=0 y = c,e* + (c,+czx)e-+e"(c,cosr +€ sinx) A B © y = c,e+…

A:

Q: (4) Does the series (1+45 converge absolutely, converge conditionally, or does it diverge?. (6]

A: As per the company rule, we are supposed to solve one problem from a multiple problem set. Therefore…

Q: Solve the differential equation dY AY dt for (; 1). vm - () 3 Y(0) = A =

A:

Q: In the function P(x) = x² + 16, what is P(-4i) equal to? type your answer.

A:

Q: y" -y-2y 0. Assume that y, (t) = e and y2(t) = e" forma fundamental set of solutions. %3D (b) Let y3…

A:

Q: 3s - 2 Find the Inverse Laplace Transform of G (s) = 2s² – 6s – 2 A 8(1) = 3e 2 sinh cosh 13 B 8 (1)…

A:

Q: For the function y =In (1-x), determine its a. MacLaurin Series expansion up to fifth degree. b.…

A:

Q: 1. Determine the direction cosines and direction angles for à =

A: To find  The direction cosines and direction angles for the given vectors.

Q: Let {bn} be a sequence whose limit is 3. Show that if B is an upper bound of this sequence, then 3 <…

A: We will use the definition of limit.

Q: 3. In the following exercises, justify your answers using truth tables. (a) Are PV (Q A R) and (P V…

A:

Q: Given the following matrices, perform the indicated matrix operation. 1 7 8 [5 1 2 -2 -4 -6 1 -2 -3…

A: Solution

Q: 8 3 Find the Inverse Laplace Transform of 35²+12 2- 49 3 - sin7t+ -cosh (2t) 7 4 A. 4 - sin2t +-sinh…

A:

Q: The value X2 .2 ... -2 x1 + 6 x2 + x3 = 9 - X1 + x2 + 7 x3 4x1 – x2 – x3 = 3 = -6

A:

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

A:

Q: Consider a, b ∈ R where a < b. Use Denseness of Q to show there are infinitely many rationals…

A: To prove: There are infinitely many rational numbers between a and b, where a,b∈ℝ, with a&lt;b.

Q: what IS the absolute value 7 -2 +i ? a. -J5 C. I b. J5

A:

Q: Since we have sin(r +y) sin(r) + sin(y), the function sin(r) is a linear transformation.

A: We know T: V---&gt;W  is said to be linear transformation if, T(x+y)= T(x)+T(y) for all x,y in V…

Q: Tx/2+sin(ix) f(x) = V2r then = (x).

A:

Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…