Prove by mathematical induction 1+2 +2²+...+ 2n-1 = 2n - 1

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Q: Question 3. In this problem show that, if we take two different regular surface patches for the same…

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Q: eff* 8 3. (Section 17.6) Evaluate ²dS where S is the part of z² + y² = 4 between z = 0 and z=4+y.

A: Please refer to the solution in next step.

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Q: Prove that a cyclic group is abelian

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Q: √x'=7x + 5y y' = -2x - 2y

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Q: Use the divergence theorem to calculate the surface integral ]] F(x, y, z) = xye² i + xy²z³j - ye²k,…

A: The given problem is to find the flux of vector field through the given surface by surface integral.…

Q: LLL វ 2] = [5, 3]. 8 Find formulas for the entries of M", where n is a positive integer. M": = M

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not…

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Q: Let the (absolutely convergent, telescoping) series be 1 n(n+1) S= Find S. Approximate the sum S…

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Q: claurin series formula is (0) + F(0)x+0+0³+¹(0)¹ +.. 2(1-x)2 has the following derivatives. F"(x)=…

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Q: 3) Evaluate the each the definite integral below: S₁² -4 e-* dx

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Q: Use the long division method to find the result when 2x4 + 9x³ +19x² + 13x is divided by x2 + 4x +…

A: Given that: By long division 2x4+9x3+19x2+13x is divided by x2+4x+8. The expression q(x)+r(x)b(x) is…

Q: A wholesale club offers two types of memberships. The Executive Membership is $96 per year,…

A: If the two costs are same, then we must have,96-0.04x=40

Q: 5. Express the value of the given functions in the form x + iy: (a) (b) cos(3-6i). sinh (i).

A: (a) : We have to find the value of cos(x-iy) in the form x+iy Now since cos(x-iy) = cos(x)…

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Q: •11• F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top and four sides (but not the bottom) of…

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Q: ath 2110Q need it. convert the following triple integral from Cartesian coordinates to cylindrical…

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Q: 5. Express the value of the given functions in the form x + iy: (a) (b) cos(3 - 6i). (₁). sin-¹…

A: 5(c) The given function is sin-12i. To Write: the above function in the form x+iy.

Q: Consider the poset ({2, 3, 4, 6, 8, 12, 15, 20, 24, 30), ). (a) Write down all the maximal…

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Q: Problem 3. Let A = {1, 2, 3, 4, 5, 6, 7}. Write out the relation R that expresses | (di- vides) on…

A: The given set A=1, 2, 3, 4, 5, 6, 7. The relation R is defined as xRy implies x divides y. We have…

Q: 4. Exact D.E. Find the solution of the following D.E. a. (2xy-3x²) dx + (x² + 2y)dy = 0 b. (cosy + y…

A: Useful information:

Q: Exercise 5.3.4 In each case, write x as a linear combi- nation of the orthogonal basis of the…

A: Given vector  x=(13,-20,15) U = span {(1,-2,3),(-1,1,1) Now to  write X as a linear combination of…

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A: A)Sol: We have G= set of all integers  and the binary operation on G is defined by a*b=a-b , where a…

Q: A = 21 2 0 6 2 8 5 0 2 7 Find the least square solution for the system Ax=b where b = (-2,-1,0, 1,…

A: It is given that  AX=b A=2016285027b=-2,-1,0,1,2T We have to find the least square solution of the…

Q: Question 12 Use the factor theorem to determine if the given binomial is a factor of f(x).…

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Q: Z P(Z) = 27+9 -find the Maclaurin series expansion of the Panction.

A: (.)  Given function is ,                 f(z)= zz4+9 (.) Maclaurin series expansion of a function…

Q: 1. (Section 17.4) Find the work done by F(x,y) = (2-², ²+e) in moving a particle once…

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Q: Evaluate √ (21²-3ig²³) dz. where C is the straight line from z = 1+ i to z = 2.

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Q: 6C Illustration is given f: R³ R³: (x, y, z)→f(x, y, z) = (x-2y, y-2z, -x+4=) Find the basis change…

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Q: Given the following set of points: 1 1.5 2 6 2.0 11 2.5 15 3.0 26 A) Find the best exponential…

A: x 1 1.5 2 2.5 3 fx 2 6 11 15 26

Q: If u = [u₁,0,0], (a) (curlv)×ŵ=? v = [v₁, V₂,0], (b) (Ỹ·ū)ŵ=? ŵ=[w₁,W₂, W3], ƒ is a scalar field,…

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Q: Factor the following polynomials by finding the greatest common factor. 7x+49 5a^(2)-15 64-40ab…

A: The given polynomials are, 7x+49, 5a2-15, 64-40ab, 18x4-12x2. We have to factor the polynomials by…

Q: 25.3 Let X = (Xn)n≥o be a submartingale with Doob decomposition Xn Xo+Mn + An. Show that E{An} <∞,…

A: Let X=Xnn≥0 be a sub martingale with Doob decomposition Xn= X0+Mn+An. To show that EAn&lt;∞ each…

Q: Find the difference of the angles. Write your answer in DᵒM'S" form. 120°45'29" and 11°39'4" 1

A: Given angles are 120045'29'' and 11039'4''. We will find the difference between these two angles.

Q: 2. Let G be the group of all real-valued functions on the unit interval [0, 1], where we define, for…

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Q: Determine the constants c₁ and c₂ in the formula f f(x)dx c₁f(1) + c₂f(0) so that it is exact for…

A: ∫01fxdx≈c1f1+c2f0

Q: Use the long division method to find the result when x¹ x³ + 9x² - 11x + 21 is divided by x2 + 4. If…

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Q: 2. What is the cyclic subgroup of Z generated by -1 under +?

A: Let, H = &lt;-1&gt; Now, for any positive integer k,       -k = (-1) + (-1) + (-1) + . . . . . . . .…

Q: Let f(x)= 3x for every x E R. Let p(x) be the polynomial of degree at most two that agrees with this…

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Q: Find the sum of the series Solution The general term ak 6k-2 4k+1 Decompose the fraction, then a s =…

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Q: 6 Sº f(x) dx 2 =

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Q: Solve congruence equation. 19x35 (mod 141)

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Q: Find a QR factorization of the matrix A. [-6-12] 17) A = 17) A 3 36 0-12 18) A- 01 1 10 -1-11

A: We have to find the QR factorization of the matrix

Q: (b) Prove, using mathematical induction, that 12 | (7"-3n+¹+2) for all natural numbers n ≥ 0.

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Q: steph is fixed, show that both 3-terms Newton forward interpolation formula and Lagrange…

A: We have been given a table of data, x x1 x2 x3 x4 x5 f f1 f2 f3 f4 f5 where x lies between…