2. Using triple integral to find the volume of a solid whose base is the region in xy-plane (z = 0) and height is the surface z xy and bounded by the curve y = 4 - x2 and the line y = 3x.

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: 2-X Evaluate the integral . S* dy dx using polar coordinate 0,

A: In polar coordinates  x=r cos θy=r sin θdxdy=r dr dθ

Q: Find the Volumes for the fallowing solids whose heights ave defined by ECX y) and bases are the…

A: Volume bounded by the region

Q: Evaluate cxy)dA av)d4 over the region R bounded by y = 2r, y=x+1 and x = 3. (3, 6) 5.5+ y-2x 4.5+…

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Q: Q2) Solve the D.E xdy + (2y-x* + 3x)dx 0

A: To solve the given differential equation.

Q: Learning Task I. Use the figure at the right to complete the inequality statements: 1. m21 3. If the…

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Q: A couple needs $50,000 as a down payment for a home. If they invest the $35,000 they have at 4%…

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Q: ř (-1)" V2n2 + 5 Given: power series (x + 1)" n=1 i. Determine if the resulting series of constant…

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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: Given the power series: +00 (2x – 1)" Σ V4n + 1 n=0 A) Solve that the provided series is…

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Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: x²y" + x(1+x)y' – (1 – 2.x)y = 0. II

A: Given differential equation is x2y''+x(1+x)y'-(1-2x)y=0           (1) By Frobenius method, let the…

Q: Q4) Find plane area inside the polar functionr = 2 and outside the polar function sin -0) +1 in…

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

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Q: Question 7 . S+2 Let F(s) =- 1 and f(t) denote the inverse Laplace transformation of 3 S+ 2 4 F(s).…

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Q: +o0 Consider the power series 22n (2x- 1)". Vn2 +1 n=1 3. Determine the radius and interval of…

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Q: 10 Given the matrix G =| 5 51 201 and do =| Then do and d, are not G- %3D conjugate if dį is given…

A: We want to find vector which is not G - conjugate to given matrix and vector.

Q: Find all integer solutions (if any) of the following Diophanti- ne equations. 1. 43x+64y = 1

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

A: Volume bounded by the region

Q: n=1 Vn + termine the radius and interval of convergence of the power series. termine the largest…

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Q: -2n2n 2n n 2) п En=1 1 —

A: Given series is ∑n=1∞1-2n2nn2n

Q: Through polar coordinates, evaluate ∬cos(x2+y2)3/2dA  where R is the region enclosed by equations…

A: Polar coordinates are related with cartesian coordinates with the following relations x=r cosθy=r…

Q: The shaded area of figure is besc described by O A (Complement of A) O AUB' O ANB' B Nane from the…

A: 1. From figure we can see the shaded region is part of A which is not contained in B. Hence Answer:…

Q: Convert dzdydx /9-x-y Into an integral of cylindrical coordinates

A: To convert into polar coordinates.

Q: 2x + 2xy2 y + 2x²y dy dx ||

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Q: Given do -[ and d = . Then do and d, are G- conjugate if G is Non of these O D B O A

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

Q: II. Consider the sequence (n + 2)! n=1 a.) Show that the given sequence is monotone. b.) Use the…

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Q: U& Newtans Method with XI=1 to find the root of theequation x²-X=4(rand tò Siy.deamaH Solve the…

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Q: Evaluate the Inverse Laplace Transform F(S)=T51)² -2

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Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Q: Laplace and Inverse Laplace Transform 1. L{ †3 – 12 + 5t + 2}

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

A: Given step by step explanation

Q: Question 1 Let y be the solution of the Bernoulli differential equation dy yx =y +x*, x >0, y > 0,…

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Q: Determine whether the following series converge or diverge. 4+ cos? n (5 – 4(In n)³)" Σ | 3n – yn…

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Q: 4 - 2v2. R

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Q: Sketch the curve. -) r=1-3cos O

A: We have to sketch the given curve .

Q: Use the algorithm for finding A to find the inverses of the matrices shown to the right. Let A be…

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Q: If C is the circle |z|=4 evaluate Sf(z)dz for each of the following functions using residue. (a)f(2)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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)…

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Q: Determine whether the following series is convergent or divergent 3- Vn (a) Vn3 n=1

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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…

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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: Given the matrix G -K and de = Then do and d, are G - conjugate if d, is given by Non of these

A: We know that,  Two vectors u, v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0  (Here…

Q: uate the integral fdy dx using polar coordinate

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

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Q: Let an ;in 2 1 In(2" +1)' Determine if the sequence {an}n=1 is convergent or divergent. Determine if…

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Q: +o0 Consider the power series 22n (2x- 1)". Vn2 +1 n=1 3. Determine the radius and interval of…

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Q: The shaded area of figure is best described by U B O (AUB)'u (ANB) O B' O (AUB) N (ANB) O ANB' None…

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Q: Q3) Evaluate triple integral f S dz dx dy.

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Q: Given: a, = In(n + 1) – In(n) for n E N %3D - {an}n=1 1.

A: