b) Given f (x)= In x x>0. Use differentiation to find the value of f'(x) at x= 2. Give your answer in 4 decimal places.

Q: Evaluate the following sum of iterated double integrals 1 2y c4-2у Ar-z dx dy + 4x-x2 e Az-a dx dy…

A: Due to  change of order we get a single iterated integral and easily it can be evaluated.

Q: Let S be the solid inside the sphere p = 6cosøand below the cone 0 = 7/4 Set-up the iterated triple…

A: Here, we are given the solid S inside the sphere ρ=6 cos(ϕ) and below the cone ϕ=π4. Now, we will…

Q: The polygon shown is concave.

A: Here the given polygon has 4 sides. We are to show that the given polygon is concave.

Q: (b) Repeat part (a) using a left endpoints. L-27 L6= 28 5 Sketch the curve and the approximating…

A: Draw the rectangles for left Reimann sum.

Q: -(ソー1ー号)

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

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Q: using polar cordinade to thd iasde -fnj +x. area

A: Area using polar coordinates is given by A=∫∫A r dr dθHere x=r cos θy=r sin θx2+y2=r2

Q: Consider the quadr atic form f (x1, 22, æ3) = x} + æ% +7æ% + 22x1æ2. (i) The maximum value of f(x)…

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Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: Here we will cylindrical co ordinate system to parametrize the surface  x=r cosθ , y = r sinθ , z=z

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

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Q: Consider the solid bounded by the planes: z=x+y, z=12, x=0, y=0. Determine the volume of the solid.…

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Q: H-w.4 Find the Volumes for the fallowing solids whose theights are defined by ECX,y) and bases are…

A: Volume bounded by the region in xy-plane

Q: Find a parametrization, using cos (t) and sin(t), of the following curve: The intersection of the…

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Q: Let V = R? and let H be the subset of V of all points on the line -3x + 4y = -12. Is H a subspace of…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Suppose the amount of a certain radioactive substance in a sample decays from 3.60 mg to 800. pg…

A: We have to find the half life of substance.

Q: inside r=2 fnd quader. ) area Find oud side r=2co in

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Q: In parts (a) and (b), find the volume of the wrinkled sphere or bumpy sphere. These solids are used…

A: Given that (a) Equation of wrinkled sphere =ρ=1+0.2 sin8θsinϕ0≤θ≤2π,  0≤ϕ⩽π, 0≤ρ≤1+0.2 sin8θsinϕ In…

Q: Find the real eigenvalues of the matrix [-11 -14 -10 1 -1 A 4 -1 6. 3 4 -1 4 The real eigenvalues…

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Q: Consider the inner product space (P2, (,)) with the inner product (p(t), q(t)) = p(-1)q(-1)+p(0)q(0)…

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Q: The system 4х + 20 y 19 z 1 %3D 5х + 26 y 27 z 4 %3D 4 x + 20 y 20 z 4 = has the solution x = , y =…

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Q: - 6х -Зу +5z 50 —Зх -2у -4z бх -3у —4z -34 = X = y = z =

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Q: Solve: (dy/dx)? + (y– 1– (x/y)) dy/dx – x/y(y – 1 ) = 0

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Q: If 21 = 22 = 23, 24 = 25, and mz4 = mz3 + 10°, What is m25? m25 =

A: Given that: ∠1≅∠2≅∠3, ∠4≅∠5 m∠4=m∠3+10o To find: m∠5

Q: 1. Let V be the region between the two spheres x2 + y? + 22 x2 + y? + 22 = 2 for z > 0. Let S be the…

A: The solution is below.

Q: Consider the vector-valued function F(2,) = [xy² + 2ye* х, у y 3xe-y Which of the following are NOT…

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Q: Maximize. z= 2x, + X2 Use the simplex method to solve the linear programming problem. X, +5x2 s 12…

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Q: Question For the equation given below, one could use Newton's method as a way to approximate the…

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Q: Consider the solid bounded by the planes: z=x+y, z=12, x=0, y=0. Determine the volume of the solid.…

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Q: The integral f(x)dx is transformed into f, 9(t)dt by applying the change of variable:

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Q: Find the eigenvalues and eigenvectors of the matrix A 0 -3 0 -8 and and d3 = b3 = || ||

A: Given matrix is A = -3010-30-40-8

Q: k 0 0 0 1 0 If A = 0 0 1 then det (A) =

A:

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4-x from above inside x = y2,x = 4.

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Q: Evaluate triple integral S*dz dx dy.

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Q: Q1) Evaluate the integral S dy dx using polar coordinate

A: We have convert the given problem into polar coordinates.

Q: eading Question 4.1.1. Which of the following maps is a group homomorphism? (Select all that ply.)…

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Q: d²N Solve t di? dN - 2t- dt + 2N = t In t

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Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9 2…

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Q: -2 -3 Are the vectors -3 -4 -8 and linearly independent? -6 3 linearly dependent If they are…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 – x from above inside x = y? ,x = 4 .

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Q: Using either Comparison Test Test, determine whether the series converge or diverge. or Integral Σ…

A: Note:- To check the given series is convergent or not it's better  to apply Root test then…

Q: salvepE tany= Sin(2 +y) +Sin(x-y) (ans. secy= C-2 Casx)

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Q: company wants to have $40,000 at the beginning of each 6-month period for the next 4 1/2 years. If…

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Q: Hw.4 heights ave defined by ECX,y) and bases are the regions bounded by the fottowing fon ttion in…

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Q: 6. Find a prime number p for which the equation x2 = -1 mod p has no solution.

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Q: 4) Solve D.E

A: Solve the homogeneous differential equation

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

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Q: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for…

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Q: Find the special solution to the following partial differential equation: (D + D'-1)(D + 2D'-3) = 4…

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Q: Let f(x) = sin(x). Suppose that h and k are two functions such that W (x) = cos(x), k'(x) = f(x +…

A: Let us solve the differentiation and integration based problem in the next steps.

Q: What is the solution of D.E (D2 - 2D)y = e sinx when solved using the method of undetermined

A: