1. Condense and expand. a) Condense as a single quantity: 1 In(3)+- In(x? +1)-3 In(1+x) 3 b) Expand: x² +1 In Vx+2(1+x)°,

Q: Given that p, = x² +xy, calcultae p, ds, over the region, y <x,0 <x < 1.

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Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: Calculate the area of the given quadrilateral starting at A and going counter - clockwise using the…

A: Use the formula and substitute the values then simplify.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,2,0), and (0,0,4)

A: # Given integral is      ∫∫E∫ zdv

Q: Evaluate 3zdV E where E is the solid enclosed by z = 1 and z = x + y

A: we need to evaluate the given integral about the solid E . first we will find the limit of the…

Q: What is the image of the vertical strip  {zϵC:−1<Re(z)<1} under e^z

A: A  conformal map is a one-one and onto analytic map. So, Re(z)=1 to a point. Here f1 is defined by,…

Q: Since Cov (X, Y) = E [X, Y] -E [X] E [Y]. Obtain Cov (Yi, BO)

A: From the given information, Consider, the regression equation be assumed as given below:…

Q: Evaluate / / /3zdV E where E is the solid enclosed by z = | and z = = x² + y?

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Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: Exercise 2 Given: BD bisects ZADC ZA = ZC Prove: AB = CB B.

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Q: Among all rectangular boxes defined by the inequalities 0 ≤x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1, find the one…

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Q: find the missing measure of H,Z, J?

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Q: Let G(u, v) = (, uv). Use the Change of Variables Formula to compute the area of the image of [1, 4]…

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Q: Find the values of a, b, c, d, e, f, g and h such that ax, S(x) = { 6(x – 2)³ + c(x – 2)² + d(x – 2)…

A: GivenS(x)=ax3,0≤x≤2b(x-2)3+c(x-2)2+d(x-2)+e,2≤x≤3f(x-3)3+g(x-3)+h,3≤x≤4such that S(x) is a natural…

Q: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: Under a change of variables z = u°/3, y = v²/2 , the infinitesimal element of area dædy becomes 6uv…

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Q: 1. Find the area of the part of the planer+ 2u + 3z = 1 that lies inside the cylinder x2 + y? = 3.

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Q: Csc? %3D 2cotx

A: csc2x2cotx=csc2x

Q: Given: ZB ZD Prove:A ABC -A EDC в Ma com A D

A: Explained below...

Q: A natural cubic spline S on [0,2] is defined by |So(x) = 1 + 2x – x³, S(x) = if 0<x< 1, |Si(x) = 2 +…

A: Given Sx=S0x=1+2x-x3if 0≤x&lt;1S1x=2+bx-1+cx-12+dx-13if 1≤x≤2

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), and (0,0,4)

A: x varies from 0 to 1&amp; y varies from 0 to 2 and z varies from 0 to 4.

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: The norm of the set {cosh(i nn x},n E N, –-2<x<2 in the Hermitian sense is:

A: Given,                  cosi nπx, n∈ ℕ, -2≤x≤2

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,3,0), and (0,0,5)

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Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

Q: Region ¥=1=sino jn 1-st q4adrant enclosed by the eardieid

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Q: Consider the solid lih S,: X=4-y² そ=2

A: Surface: Surface, A two-dimensional collection of points (flat surface), a three-dimensional…

Q: Under a change of variables æ = u², y= v³ , the infinitesimal element of area dædy becomes 3u?u°dudv…

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Q: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: 2. Which of the following statements is TRUE about rectangle WXYZ. X z, 10 Figure 1 WV = VZ XZ XY O…

A: Given query is to find correct statements for the rectangle WXYZ.

Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: 13-Evaluate JJI zdV E where E lies between the spheres x2 + y? + z2 = 1and x2 + y? + z? = 4 in the…

A: The given integration is , Let, I=∫∫∫EzdV change the integral into spherical coordinates Put x=r…

Q: let A and B be matiices of Con det A) = -1 find the Valué of Cdet(z AT) - dct(-2B )) LA Pproxi mate…

A: Given:- det(A) =-1/2   ,  det(B) =2/3 To find:- [det(AT/5) -det(-2B-1)]2

Q: Find the angle between x and x4 in C[0,1] with its standard inner product.

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Q: EXAMPLE 6 Find the volume of the box (parallelepiped) determined by u = i+ 2j – k, v = -2i + 3k, and…

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Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

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Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1)

A: We need to find the x coordinate and y coordinate of the shaded region which is bounded by two…

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,6,0), and (0,0,3)

A: This question is related to triple integral, We will solve it using given information.

Q: Find the enclosed by. Volume r= 2cos 6 ×*+ッ+2- 4 .

A: Find the volume

Q: What solid is formed when this net is folded? A C D

A:

Q: b) Give a partition which divides I = [1,2] into n equal parts. %3D

A: Consider the Interval  [1,2]

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,1)

A: We have to find the volume integral of the given function.