Discuss following series : 3. +. 4 4 (i) +... o (x > 0) (n+1)" x" (ii) E 2 33 3 3 (iii) 12 1 44 4 +. 23 3 +... ∞ 34

Q: Solve the initial-value problem 1. y"-3y'-10y = 0, y(0) = 0, y'(0) = 7.

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

Q: The problem of the firm can then be written as max {7 [f(n,) – (1+r)b,] + (1 – 7) [f(øn, +n¡) – prn1...

A: This is the problem of multi variable calculus.

Q: t ,0st<2 A. Given f(1) =- L{f(1)}. obtain L 1".122 le,t22

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Q: Evaluate the integral by reversing the order of integration. 16 dy dx y³ + 1

A: From the given problem, it is observed that the region of integration is x,y: x≤y≤4; 0≤x≤16. Draw th...

Q: 1. y" – 2y' = sin 4x 2. y" + 6y' + 9y = 1+x 3. y" + 2y' + y = xe-* 4. y" + y = e* + x3 y(0) = 2; y'(...

A: 1.) y''- 2y'= sin4xAuxiliary equation is m2-2m=0⇒m(m-2) =0⇒m=0, 2y(x)= c1+ c2e2xPI= sin(4x)D2-2D= si...

Q: Let V be the volume of the solid that lies under the graph of f(x,y) and above the rectangle given b...

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Q: Express 50 C30 as a sum of two terms from Pascal's triangle, each in the form Cr. O 51 C30 +51 C31 O...

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Q: Show that (a) p → (q →r) # p-(-qv r) (p^q) →r (b)[-p^(-qAr)]v (q a r) v (p ar)

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Q: 3. f(x) = x In x - 2x + 3 on (0, ) . f(x) = -12r + 75x* – 80x . f(x) = x² - 2 In x %3D

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Q: L 3 S

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...

Q: 1) L-1 3 S 1 2) L 48 2 S 5 S (s +1)* 3) L-', 4 S 1 1 1 4) L-', 2 S S s- 2 1 5) L', 4s +1

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Q: 3. Use the transformation u = 4, v = xy to find || ry³ dA over the region R R in the first quadrant ...

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Q: Find the solution to the following system of equations: -4 1 X1 - 200 1 -4 1 X2 -400 1 -4 1 X3 1 1 -...

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Q: (5) Solve the diffusion equation with dissipation: U - Dugr = bu, -0 <x < ,0 <t <0 with initial cond...

A: A general diffusion equation with constant dissipation with initial condition is of the form: ut-Dux...

Q: 3. A particle of charge q = moves in velocity i = (2 + m)i – (5 + m)j – 4k in magnetic field B = (7 ...

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Q: Find the solution of the system of linear equation and the value of the determinant of its coefficie...

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Q: What are the first 5 entries in row 100 of Pascal's Triangle? O 100 C1, 100 C2, 100 C3, 100 C4, 100 ...

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Q: 4. Find all the roots for each expression. (a) (-1)4

A: This is the problem of complex analysis.

Q: Solve for x. If necessary, round to the nearest ten-thousandth. (If there is no solution, enter NO S...

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Q: Isosceles triangles were used as the main geometric figure in the patches used to make a tent. The e...

A: Area of isosceles triangle = 12×a×b×sinθ, where θis the angle between the sides with length b and c....

Q: The following is correct application of Hypothetical Syllogism: [RƆ (QƆ S)] Ɔ (C V D) (C V D) Ɔ (QƆ ...

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Q: Given matrix : (1 c+2 _d-12 A=|0 7 0 5 3 b=-2 and vector: a) Calculate the inverse matrix: using the...

A: We have to find the A-1 using Gauss -jordan method .

Q: Find L{f(t)}using the First Shifting Theorem. Note: a, b, e, w, k and n are constants. 1. L{Se" sin ...

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Q: The sum of an integer and 4 less than that integer is even.

A: If an integer is divisible by 2 then it is even.

Q: Using Reciprocal Substitution * For S Option 1 Option 2

A: We have to use reciprocal substitution for integration.

Q: : Find the PA=LU factorization of the following matrices: 2 4 -2 2 4 -2 A = 6 0 3 B = 6 0 4 2 3 4 2 ...

A: Here we will use  Gaussian elimination to find LU decomposition  In PA=LU ,  P is identity matrix  N...

Q: Question2. Find the equation of the line which is perpendicular to the line 3x – 4y – 12 = 0 and pas...

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Q: Verify that the given function u is harmonic in an appropriate domain D. Find v(x, y), the harmonic ...

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1. Th...

Q: 5- Verify that the given function u is harmonic in an appropriate domain D. Find v(x, y), the harmon...

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Q: Question1. Find the vertex of the parabola, y = f(x) = -3x2 + 6x + 3. %3D Inntationa for

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Q: Show that F(x, y) = x² + 3y is not uniformly continuous on the whole plane.

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Q: Evaluate (2y + 1) dS, where S is the part of the plane 2x+2y+z=6 that lies in the first octant.

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Q: Evaluate F dr, where F = (-6x²,9y², –12z?), %3D and C is the curve: 7(1) = (t, t? – 2r°, 21' – 1²), ...

A: Differentiate the expression of r→(t)=t,t2-2t3,2t3-t2 to obtain the expression of dr→. The power rul...

Q: . Prove that there is no distinction between contravariant and covariant vectors if the transformati...

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Q: Evaluate the integral, if it exists: lim sinx dx r→+z -r

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Q: Func tion FC<) = _4 *+4 2)find a the the %3D power series por Cen lered c= 1 and de termine the in t...

A: Power seriese and interval of convergence

Q: Se f(x, Y, z) = (x² + y² + z²)¯iwe can say that + a²r ' a²y a²z equals to Choose an option O a. V f(...

A: Given function f(x,y,z)=(x2+y2+z2)-12. We have to find the value of ∂2f∂x2+∂2f∂y2+∂2f∂z2. Formula wi...

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x² – x - In(x) (a) Fin...

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

Q: of matrices

A: Given,             A=124-3 and   f(x)=2x3-4x+5,          g(x)=x2+2x+11

Q: Show from first principles, Le., by using the definition of linear inde- pendence, that if µ = z + i...

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Q: zdz ,Z = (2z+1)3 For f O z = u^(4/3) O z = u^(1/3) O z = u^3 O None of the choices O O

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Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector pr...

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a, ...

Q: The following data for the velocity component in the x-direction, u, are obtained as a function of t...

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Q: Evaluate the double integral. I1, 7y? dA, D is the triangular region with vertices (0, 1), (1, 2), (...

A: We need to find  double integral , ∫∫D7y2dA  , where D is the triangular region with vertices (0 , 1...

Q: Problem: The velocity of a moving particle was recorded at four instances as shown in the table belo...

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Q: Let M1 = ( S1, Ih) and M2 = ( S2, I2) be two matroids with disjoint ground %3D sets. Prove that the ...

A: Given: Two matroids M1=S1,I1 and M2=S2,I2 with disjoint ground sets.   To prove: The subset system M...

Q: 3cjs100°) (2cjs10°) Express in rectangular form. -2 (4cjs50°)

A: The rectangular form of a complex number z=a+bi and polar form is z=rcosθ+isinθ, where r=a2+b2 and θ...

Q: Solve for x. If necessary, round to the nearest ten-thousandth. (If there is no solution, enter NO S...

A: Given expression is log6x + log6(3x - 2) = log621

Q: 7. In a chess competition involving some men and women, every player needs to play exactly one game ...

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Q: The table below shows the six basic solutions to the following e-system. The nonbasic variable(s) in...

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