Use polar coordinates to evaluate sin (2² + y²)³ dA, where R is the region enclosed by the curves with polar equations 0 = 0, r = ñ, and r = 0, as shown below. 24 2

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…

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

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Q: 8. 1 3 5 k Let A If the dimension of the eigenspace corresponding 0 0 8 5 0 3 to eigenvalue 8 is 2,…

A: We have A=813705k400850003 Now for eigenvalue 8 we find the eigenspace. Consider:…

Q: Suppose that five good fuses and two defectives have been mixed up. To find the defective fuses we…

A: Given: Good fuses are 5 Defective are 2. Total becomes 7 fuses.

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…

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Q: Question 8 Let B = {b1, b2} be a basis for a vector space V. Let T : V > V be a linear…

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Q: 300r Integrate numerically: f (x) = 1+e from 0 to 10 using 5-segment trapezoidal rule. Round-off the…

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Q: Question 23 Let H dimH? Span{1+x, 1+a, 2 + a + x2, 3 + 2x + a}. What is

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Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: Usng polor Codirte to Sad ared bourded by ブニリ ブ=ス

A: Here we use basic polar coordinates to find this.

Q: EVALUATE THE LAPLACE TRANSFORM OF THE GIVEN FUNCTION USING APPROPRIATE THEOREMS. 1. f(t) = et+1 cos…

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Q: (NAS 4) Given, A = x²zî – 2y°z²j + æy?zk Find divAat the point (1, –1, 1)

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Q: Given de - and dy = . Then do and dq are not G- conjugate if G is Non of these 12 O A 0.5 0.25] [18…

A: We want to find matrix for which vectors are G conjugate

Q: See equation below. Find: a + b -c+ d. (Answer must be an integer) The system x' + y = t; 4x + y' =…

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Q: Question 33 You are given that B = {1+æ,1 – x², x + 2x²} is a basis for P2 and [p(a)]g = 3. If p(x)…

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Q: Let n = pq be the product of two odd primes. Recall that there are no primitive roots modulo n. Show…

A: We use the idea that if primitive root exists then x^2 = 1 mod (m) has only 2 solutions. The…

Q: (iii) If u = 461 + 362 and [u]c = then the value of r is and the value of S is (iv) If V = 3c1 + 2c2…

A: Given that  b1 = 10c1 +3c2,  b2 =27c1 +8c2 c1 =-8b1 +3b2,   c2=27b1 -10b2

Q: [1] Construct a 2 × 2 symmetric matrix A such that A 3 and -2] -2 8 a11 012 If A = a21 then the…

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Q: 5. Use the method of Lagrange multipliers to minimize f (x, y) = x2 + y? subject to 2x + 8y 102.…

A: The given question is related with Lagrange multipliers . We have to minimize fx , y = x2 + y2…

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

A: let B={b1,b2} be basis for vector space.

Q: cos?. z=1 s divergent or convergent?

A: Given series is ∑z=1∞cos2πz

Q: Example 7 Sketch the curves (a) r 1 (b) @ = 4. %3D in polar coordinates.

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

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Q: 2. Let f be defined on an open interval (a, b) and assume that for some e e (a, b) we have f'(c) > 0…

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

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Q: 1 List the elements of each of the (a) The set of integers between 1 and 50 that are divisible by 8…

A: a) Set of integers between 1 and 50 that are divisible by 8 is: S=8,16,24,32,40,48

Q: Wu's job pays $17/hour, and requires him to be at work at least 29 hours/week. He is allowed to work…

A: Solution:Budget line:C = 17h for h⩽40(1.5) (17) (h-40) for  40 ⩽h⩽602(17) (h-6) for h⩾60

Q: Question 34. Let A be a symmetric matrix. Suppose that u and v are two eigenvectors of A…

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

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Q: 1 + 4 = 5 2 + 5 = 12 3 + 6 = 21 8 + 11 = ?

A: Solution :  Given that  1 + 4 = 5  2 + 5 = 10  3 + 6 = 21  8 + 11 = ?

Q: 17 37 Consider the orthogonal basis B = -3 10 of R³. -3 1 -9 11] Let V = -16 7 а If vB= |b|, what is…

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

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

A: Eigen values of the Matrix are

Q: In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the…

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

A: Given step by step explanation

Q: You are given that B= {1+2x², 1 + 2x + 3x2, -8x – 5x2} is a basis 5 for P2 and [p(x)]B = 4. If p(x)…

A: The solution is given as

Q: 3 0 07 Let A = |0 3 0 3 1 Which of the following statements is TRUE about the quadratic form f(x) =…

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

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Q: Prove or disprove the following cases: (i) If x E Q and p € R – Q, then x+p€R – Q. (ii) If x E Q…

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Q: 1 Let A be a 2 × 2 symmetric matrix satisfying A 9. and 2 -2] A 1 [1] with the spectral…

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Q: 4. Evaluate the integral I 1 sin? x dx Include 4 decimal places on your 3 computation. a. single…

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Q: onsider the power series 22n (2r- 1)". Vn? +1 n=1 1. Use alternating series test to show that the…

A: Typewritten answer in latex is presented below.

Q: -B-B- 1 and W =Span{u1, U2, Uz}. For Let U1 %3D , U2 = Uz = 0. 2 -2 in W ? what value of t is the…

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Q: Question 4 Consider the function 3zy 3 + y? (a) State the domain of f(z, y). f(I, y) (b) Find the…

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Q: ind the longes PtaV + (In(z- 2) )y = 0. y(3) = 1 and y(3) = 0

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Q: 1 1 Let A = 2 1 . Find a QR-factorization of A. If R = [1 3 then the value of a is the value of b is…

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Q: E Very continyous Ronction fi [aib}ng R is Riemann integkable.shewthat the conkerseis not trup.…

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Q: 2. Using triple integral to find the volume of a solid whose base is the region in xy-plane (z = 0)…

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

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Q: Question 11 8. 1 3 7 k 4 Let A = . If the dimension of the eigenspace corresponding 8. 0 0 0 3 to…

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