1. Consider the following intervals on R: A = (0,1); B = (1,2); and C = [2,3). For each pair of these sets, which is separated and which is not.

Q: Eliminate the arbirtray constants

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Q: II. Consider the function g defined by 1 g(x, y) = cos (x# /) + logg (r - y) Do as indicated. 1.…

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Q: Determine whether the vector field F(x, y, z) = (y + z)i – xz°j + (x²siny)k is free of sources and…

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Q: Evaluate: , asirnadz using a 3rd level (k=3) Romberg integration. Round off to 6 decimal places.

A: Use the following formulae, to estimate the definite integral ∫abfxdx by the Romberg integration…

Q: d’u Find solutions u, =F,(x)G,(1) of corresponding to zero initial velocity and satisfying boundary…

A: Consider the given differential equation, ∂2u∂t2=-c2∂4u∂x4      ⋯1 Let us consider that…

Q: 19. Find the general solution of the system of differential equations (2)-( )(:) Sketch the phase…

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Q: Verify the formula $ F. T ds = || (curl F) · n dS in Stoke's Theorem by evaluating the line integral…

A: given curve Fx,y,z=9x-5y i +9y-5z j +9z-5x k verify the formula ∮C F·T ds=∫∫σcurl F· n dS in stoke's…

Q: Question 5 Solve the following initial value problem using Laplace transform y" – 4y' = 8, y(0) = 0,…

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Q: A stone is dropped from the top of a tower. it reached the ground in 2 s. what is the height of the…

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

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Q: Using Variation of Parameters, the particular solution y, of the non-homogeneous differential…

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

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Q: [5 2 0 similar to B; if no, explain why not. Let B = Is the matrix B orthogonally diagonalizable? If…

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Q: A' D A C' E b В H a

A: Consider △ABC and △HEC,

Q: Verify the Divergence Theorem by evaluating F.N ds as a surface integral and as a triple integral.…

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Q: The equation p =- in spherical coordinates 5 represents sphere.

A: This is a problem of spherical coordinate system, vector calculus.

Q: 5. (a) Let V = R* and let (·, ·) be the standard dot product on V. (i) Calculate (e, +€3; €2 + €4).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Use any method to determine whether the series converges. k2 (a) k3 + 6 Vk (b) k3 + 6 ?

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Q: Use resolution to show ∀x∀y[p(x,y) → ¬p(y,x)] models ∀x¬p(x,x)

A: Please look into the next step for detailed answer

Q: 1. Consider the circle in the ry-plane given by the parametrization x = 2 cos t, y = 1 +2 sin t, 0…

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Q: 4. Let f:A-→R and g:B–→R where f(A) CB. Explain to prove that if f is continuous at Ce A and g is…

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Q: 1. Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

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Q: (1 3 1 2 2 A = 2 3 1 B =1 4 2 2

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Q: Describe the graph of the equation. r = 16costi + 6 sintj – k O It is an ellipse in the x = -1…

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Q: Solve the following surface integral (use definition): F = [32 6 6rz] with parabolic cylinder…

A: Given, F = 3z2i +6j + 6xz k And surface S is ,S:y= x2  with 0 < x < 6 and 0 < z < 1…

Q: (a) Evaluate the triple integral z dV, where E E= {(x,y,z):0<x< 3, 0<y< 3, 0<z< 2).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: We consider the linear transformation T1 : R3 R 3 T1(x,y,z) = ( x +2y –z , x –y +2z , x + 3z) We…

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Q: 1. Find the area of the region bounded by the curves y 3D x3 — 5х + 6, у %3D 10 — 4х — 4x2 and the…

A: To find the common area :-

Q: From the particular solution of the DE y" + 2y' + y = x at x = 0, y = - 2,  y' = 2, obtain the value…

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Q: y = 5/(sin3x +cos3x)

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Q: Investment Mixture A sum of $20,000 is invested in three mutual funds. In one year the first fund…

A: Given: Total investment =  $20,000

Q: Suppose f : A → B is an injective function, and {A;};e1 is a partition of A. Prove that {F (A;)};er…

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Q: faow that the function f depthed by (X .Y) = (1, - 1) f(XrY) = %3D x2 + 냉 (x, y) $ (1,-1) * ty is…

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Q: Prove whether the pollowing series converges and state which theorem diverges. to prove. or you use…

A: Convergence of the series

Q: Without the aid of the Wronskian determine whether the given set of functions is linearly…

A: Given functions: f1x=lnx and f2x=lnx2 To show: Determine whether f1x and f2x are linearly dependent…

Q: Consider f(x) = eª, 0<x< T. (a) Find the half-range Fourier sine and Fourier cosine expansions of f…

A: Given: Let us consider the given fx=ex, 0&lt;x&lt;π a) Determine the half-range Fourier sine and…

Q: 15. Which of the following is an even function of t? t-sin(t) t'cos(t) sin(t) +t t'sin(t)

A: The function is said to be even if f(-t)=f(t) The function is said to be odd if f(-t)=-f(t) Note:…

Q: Y r = 4 sin 0 r = 1+ sin 0 B 2. Consider the polar curves (see figure above) r = 1+ sin 0 and r = 4…

A: Using the given picture. A and B lies in first and third quadrant so the angle lies between 0 and π

Q: a, A function, f(t), with period 2n is given as f(t)= +E[a, cos(nt)+b, sin(nt)]. n-l The term [az…

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Q: Solve the following system of differential equations. dx 6х + Зу — 82 dt dy 2y dt dz = x – 3z dt

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Q: What is the distance between the line with Cartesian equation x-2 = y-8 = z-3 and the line with…

A: If first equation of the line parallel to the vector V1 through the point P1 and the second equation…

Q: [B] Use Newton-Raphson Method to perform thirteen iterations to the equation f(w) = w* + 4w² – 10 =…

A: This is the problem of Numerical analysis.

Q: Given the digraph: a b.

A: 1. The ordered pairs are  a,a,a,b,b,a,b,b,c,a,c,c,c,d,d,d

Q: Let / be the line given in parametric form by the equations x = 1 + 21 y = -1 + 31 z = 2 + 51 What…

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Q: Solve (x-j2y) + (y-j3x) = 2+ j3

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Q: 3. u, = u, - sin x cos t, 1 >0 В.С.: и(0, г) %3D0, = () 1.С.: «(х, 0) %3D 0, u,(x. 0) = 0

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Q: Differentiate Зх — 6 - y = csc 5x2 + 9

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Q: Determine the general expression for the four roots of V3 – j . O V2cjs (- + 글세), k=D 0, 1, 2,3 O…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-