(1) Find A, B, C, make the algebraic precision of the quadrature formula [f(x)dx = - Af (0)+ Bf (0.5)+Cf (1) as high as possible.

Q: Let an ,n 2 1 In(2" + 1) divergent Determine if the sequence {an}n=1 is convergent or

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Q: Consider the power series > 22n (2x – 1)". Vn2 +1 n=1 Use alternating series test to show that the…

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Q: 4. Determine the general equation of the plane containing the points P(1,-4,-5), 3 Q(2,0, 13) and R|…

A: Let the equation of the plane be        ax + by + cz + d = 0 . . . . . . . . (1)  (1) passes through…

Q: 2. Solve the following differential equations: (a) y' e2y = (b) y' = 1+ Y (c) xy' = y(3 – x)

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Q: Consider A = (0, 4, 2) , B =, (6, –1,0) and C = (3,0, 1). (a) Find the unit vector having the same…

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Q: dy dv S.S; as sin ny dedy Cii)

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Q: Does it converge or diverge? Σ 2 + 2n' n=2

A: Given series is ∑n=2∞n2+2nn

Q: Show clear and detailed solutions. (a) Find the general equation of the plane 2 passing through the…

A: Plane parallel to a plane ax+by+cz=d is  ax+by+cz=k

Q: Use polar coordinates to evaluate sin (a² + y²)* dA, R where R is the region enclosed by the curves…

A: Here if we put limits in order dr dθ, then the given integral can not b evaluated so we need to put…

Q: Use the method of Lagrange multiplier to find the largest and least values of h(x, y) = x2y on the…

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Q: -1 2-x Q1) Evaluate the integral , S* dy dx using polar coordinate

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Q: (D)y= cos C2x) E CCs (1) m'tm= o (2)

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Q: Eva‎luate the ite‎rated do‎uble integr‎al ∫ 3−1 ∫ 0√(3−y) e12x−x^3 dx dy by chan‎ging the or‎der of…

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Q: +oo 22n (2.x – 1)" Consider the power series >, Vn² + 1 Use alternating series test to show that the…

A: Given series is ∑n=1+∞22nn2+13(2x-1)n

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

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Q: fllowing integVals using Polar methad : yり x dy QlEValuate the

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Integrate the fallswingfuntinne aver the given regionr s R: the circle x+y=t and y=x? thiss

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Q: п(т — 2)" 3" (2n – 1)3* Consider the power series 1. Show that the power series converges when æ =…

A: Radius of converges and interval of converges for the power.

Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u eR…

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Q: Q.2 An alternating current sfter passing through a rectifier has the form f(x) = losinx , OsxST = 0…

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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 general form of AT Ax = ATb used to find the line of best fit C+ Dt throu (t1, b1),…

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Q: Question 8 Use the Laplace transform to find the solution of the following ODE y"+16y = 28(t – x)…

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

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

Q: Sheet 3 Numerical analysis QI/ Use the polynomial that fits data shown by Newton divided difference…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

A: Given step by step explanation

Q: Find whether the shown expression below diverges or converges Show your solution and how you came up…

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Q: Find the sum of the following convergent series. Σ 37+1 00 1 6n-1 n=0 Vn +1 n=16

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Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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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: Find the solution of the following IVP using the characteristic method : u + uu= y у , и(1,у) %3D Зу

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Q: - 2T -T 271 a ftt)= Cos nt Fourier Series s'i n:1,3,5,... %3B findi a+ b+ C

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Q: 4. У(п) %3D [x1(п) * х2(п)] х1(п) %3D 26(п) + 56(n-2) х2(п) 3D 46(n-4)

A: Given y(n)=x1(n)*x2(n) Where x1(n)=2δ(n)+5δ(n-2)                (1) x2(n)=4δ(n-4)…

Q: * = y +z- 4x Solve: dt = x+ 5y - z # = y - 3z

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Q: Factorise x6 + 1 as a product of three quadratic polynomials with real coefficients.

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

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Q: Show that if x is an integer, then gcd(x + 1, x2 – x + 1) divides 3. -

A: First, we find gcdx+1, x2-x+1 Now, factors of x+1 are x+1, 1 x2-x+1 is a quadratic equation of the…

Q: All New Yorkers are cosmopolitan. (N, C) All cosmopolitan people are friendly. (F) Either Tom or…

A: We have to use resolution to determine if the following arguments are valid.  We Know that,

Q: -2 1 1- 2et 0 2

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Q: (1 – 2n²)" n2n n=1 WI

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

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Q: 1 -1 Ob tai the Fruries Seriesi a Ans: fee= TT 2ntl Find; ab

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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: Given the series: k 6 8. 11 k=0 does this series converge or diverge? converges O diverges If the…

A: Given series is ∑k=0∞8·611k

Q: In(n)

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Q: Show that the odd numbers and the natural numbers have the same cardinality

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Q: Given: 3z = xy Find fy O xy/3 O y/3 O x/3 O None of the choices

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Q: Suppose f is continuous on the interval (0,3). Assume further that f(0)= -2 and f(-3)= 5. Also, lim…

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Q: If lim f (x) = 2 and lim g(x)=-1, then lim 3/(х) - 2g(х) is ... f(x)+ g(x) Jika lim f(x) =2 dan lim…

A: Limit of the rational function