Let τ be the divisor function. Show by any means that τ (n) is odd if and only if n is a perfect square.

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Q: 6) Find the determinant: -2 3 4 3 4-2 5 6-3

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Q: 1. Given the following matrices. 3 1 B-[13] A= F= Find: LO 1) A+D = 7) EG = 2 3 10) hi = 0 4…

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Q: Evaluate the limit or show that it DNE. lim (x,y)-(0,0) (x- y²)(y-x²) x¹ + y4

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Q: 16. y = X x² +9

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Q: Let A = 9 -3 k For A to have 0 as an eigenvalue, & must be

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Q: Show that the Catalan numbers count the following. (a) Sequences (1, 2,..., æn) of positive integers…

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Q: 2. Find the harmonic conjugate v (x, y) of u (x, y) = e cos y + e cos x + xy.

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Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: A. Find the exact value: 2 sin(0) de = B. Find the MID(1) and MID(2) estimates for the integral:…

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Q: Find the center and vertices for this hyperbola: 4x^(2)-9y^(2)-24x-36y-36-0

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Q: Find the points on the circle x\power{2}+y\power{2}-2x+4y-20=0 which are farthest and nearest to the…

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Q: A craftsman wants to make a cylindrical jewelry box that has volume, V, equal to 65 cubic inches.…

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Q: + Question 3 of 15 > Note: Please make sure to properly format your answers. All dollar figures in…

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Q: find the function of the form y = a sin [b(x-c)] + d with given period, phase shift and range 6, 8,…

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Q: Kirkman Brothers ice cream parlors sell three different flavors of Dairy Sweet ice milk:chocolate,…

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Q: 22. Evaluate the Laplace Transform of * L{e-2t+4e-3t) Option 1 Option 3 5s + 11 (s+2)(s+3) 5s + 11…

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Q: Decide whether the following sets of vectors span the given vector space, are linearly independent…

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Q: Find the Maclaurin series for f(x) = What is the Maclaurin series of Σ n=0 11 1+xX 11 ? 1 + x (Type…

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Q: Find the projection projuv, where u = (1,3,-2) and v = (2,-1,3).

A: Since we kow that the projection of v on u is given by                projuv=u.v||u||2u

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Q: 6. Draw the space curve given by r(t) = (t cost, t², -t sin t) for t≥ 0.

A: The given curve rt=t cos t, t2, -t sint for t≥0. We have to sketch its curve.

Q: Compute the products in Exercises 1–4 using (a) the definition, as in Example 1, and (b) the…

A: The given matrix is, -421601317. Multiplication of the matrices is possible when the number of…

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Q: If the intercepts of the variable circle on the x-and the y-axis are 2 units and 4…

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Q: . Find the angle between the two tangents from the origin to the circle…

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Q: b) Prove that if f(z) and f(Z) are analytic in a domain I, then I is a constant function.

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Q: Tabular representations for the functions f. g. and h are given below. Write g(z) and h(z) as…

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Q: Match the formula for each Legendre Polynomial. P_0 P_1 P_2 P_3 1 X [Choose ] ✓ [Choose ] x^3 -…

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Q: III Solve the differential equations (xy-6x²) dy - (2y² 9xy) dx when x = 1, y=1

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Q: Solve the following first-order differential equation (x2y+xy-y)dx +(x2y-2x2)dy=0

A: Given that the first order  differential equation x2y+xy-ydx+x2y-2x2dy=0     .

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Q: In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" +by'…

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Q: Graph the following function: X y = 3 cos (+1) +1 2 Drag the black dot to shift your graph in the…

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Q: [1 For which value of k does the matrix A= multiplicity 2? k= k have one real eigenvalue of…

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Q: 13. The interior of a set coincides with the interior of its closure..

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

Q: (3) Sketch the points (−1+ ei)¹/5 and (-1 - ei)¹/5 for € "small". Based on your sketch, explain why…

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Q: Match each equation to the conic section it creates. (x+5)² 25 a. + (y-2)² 4 b. 3x³ + 4y = 25 d. = 1…

A: a. The standard equation of a ellipse is (x+x0)2a2+(y+y0)2b2=1.So (x+5)225+(y-2)24=1  is equation of…

Q: 9) Solve the set of equations by finding the inverse of the coefficient matrix: x - 2y = 5 y = 15 3x…

A: 9. Given the set of equations                     x-2y=5, 3x+y=15.