Use mathematical induction to show that, for any positive integer n, we n have that n(n+1)(2n+1) k2 = 6. k=1

Q: 1 -8 -8 Let A = - 8 1 -8 and v = 1 Verify that 9 is an eigenvalue of A and v is an eigenvector. Then…

A: The given matrix is                       A=1-8-8-81-8-8-81

Q: Q5. A Ferg uson Curve is defined by two Points (o, o, o) audl C5,0,0) aud two tangents I 1S the…

A: Let the curve be defined by following parametric form- x(t)= at3+bt2+ct+dy(t)= et3+ft2+gt+hz(t)=…

Q: Let W= Span{(1,1,1,1), (0, – 1,1,2), (1, – 1,3,1)} | Find a nonzero vector in R* in the orthogonal…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 8t – t³, In(t))

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Q: .Let S be the part of the sphere r+y+ z = 4 located above the plane z 0, oriented at the point (0,…

A: Here we can use divergence theorem, which states that ∫∫S F n ds=∬∫V divF dvHere divF=divergence of…

Q: そ-f (xy)

A: Given,  if Z=f(x, y), and u=x-y,  v=x2-y2 To prove that                        ∂Z∂v=∂Z∂x+∂Z∂y2u…

Q: (r' x r") r" Ir' x r"|2 Find the curvature and torsion (1 = | of the curve x = 3 sinh(t), y = 3…

A: Given that x=3 sinht, y=3 cosht, z=3t So r→t=x=3 sinht+3 cosht+3t

Q: use Euter me thed to solve y's 2-24

A: Let us consider the given function y'=f(x,y), y(x0)=y0 Solving using the Euler method  Then the…

Q: determine if the points (1, 3, 3), (3, -1, 5), (5, 2, 0), and (3, 3, 4) lie in the same plane.

A: We will have to check whether the points (1,3,3), (3,-1,5), (5,2,0), (3,3,4) lie on the same plane…

Q: x3y" – 5xy' + 9y = 0 -3x y" + 5y' + 4y = 10e %3D

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Q: Find vector and parametric equations of the plane through A (1,1,-1) and B (0,-2,3) that is parallel…

A: The solution is below.

Q: Q3/ The value of k such that P2(1) = 2.8, 2 k 4 Is إجابتك

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Q: Howiy If Z =Rcxy) and u=x-yg V=x²_y show that +23 %3D

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Q: Military veterans receive a 25% discount on movie tickets that normally cost $16. Explain why…

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Q: Find the (a) true error and (b) relative error of the following: The derivative of f(x) = ln x at x…

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Q: Find the gradient vector field Vf of f and sketch it. f(x, y) = x2 - 4y Vf(x, y) = y y 6h 6 4444…

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Q: Consider the closed heart curve y(t) = |t|^3/4 *(sin(t),cos(t)) with -pi st s Tt below. (a) Write a…

A: As per your query the solution of part b is given in the next step.

Q: Compute the following product. -4 -6 8 [9 -7 -3 4 -4 3 4 -4 1 2 1 -2 9 1 7 || 4.

A: The given product is   9-7-31234-1-4-685-944-4-4121-2917 To find the above product we will use the…

Q: 2) Determine if F is a conservative vector field. If so, find a function f such that F = Vf. b. F=…

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Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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Q: Consider a Ctosed Kectangutar boxwith a Hw.4 squar bare If base side is measured with evror at and…

A: Let the side of square base is x and and height is y. given that error in x is 2% and error in…

Q: 6. Solve the initial value problem y" – y = cos(x) with y(0) = 0 and y'(0) = 1.

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Q: Consider the function f(T,y)= kr - 2xy + y?. %3D 1. Show that (0, 0) is a critical point of f(T, y).…

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Q: Let x(1) = c,cos(5 t) +c,sin(5 t) be a two-parameter family of solutions of the Let y =c,e*cos(5 x)…

A: To find which of the given option is correct, about the given differential equation :-

Q: The table and scatter plot show the time spent watching TV, x, and the time spent doing homework, y,…

A: Given that, the linear model for the given data is y=-0.3x+20.51.

Q: xInx at 0<x<1 1-X Show that the function f(x)= is integrable on the interval [0,1]. at x = 0 -1 at…

A: The problem is from Theory of Integration.

Q: cos Σ 1+1 Consider the series n n=174 O It converges absolutely. O It converges conditionally. O It…

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Q: A homeowner installed new kitchen cabinets and countertops for $6,000. He paid 20% down and financed…

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Q: Show that (p-q)–(r¬s)and(p-r)-(4-s) are not logically equivalent.

A: To show that p→q→r→s and p→r→q→s are not logically equivalent.

Q: B) Find the unique polynomial P(x) of degree 2 or less such that P(1) = 1, P(3) = 27, P(4) = 64…

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Q: Find parametric equations for the line. (Use the parameter t.) The line through (-8, 4, 7) and…

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Q: Q1. For the periodic function: f(2) = {* r+1 -1<r<0 1 05ISI Determine: 1. Is it Odd, Even, or…

A: Given, f(x)=x+1 , -1≤x≤0           1       ,    0≤x≤1 To find: a) Whether a given function is even,…

Q: srepresentation issues in the given graph. Select all that apply. 100

A: 1. the horizontal axes is scale is appropriate where each point is at the distance of 4 units  2.…

Q: Let R be a relation on the set of all non-negative integers defined by aRb if and only if a3 - b3 is…

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Q: (i) By making the substitution o = tan 0, demonstrate the validity of %3D Parseval's theorem for…

A: Consider the function as ft=e-tdt

Q: 4 9. The vector is a linear combination of the vectors and -7 if and only if the matrix 8 equation…

A: Let A be a m×n matrix then the system Ax = b has a solution if and only if b is a linear combination…

Q: Show that if U and W are subspaces of the vector space V, then dim UnW < min{dim U, dim W} . Prove…

A: Given statement is false. Counter example is as follows

Q: Determine f(5) if f is a continuous function that satisfies t 4x+sin(rz) f(t)dt = x for all z. %3D

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Q: • Use False Position Method. Compute Es according to 4 significant figures according to the formula…

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Q: Which quadratic function has the largest maximum? (1) h(x)= (3- x)(2+x) (3) k(x) =-5x² -12.x +4 (2)…

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Q: Q1/ Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75) =…

A: using newton's backward difference formula find the approximate value of y-13 given y -0.75 -0.50…

Q: Discuss theConvergence o the following

A: As per our guidelines we are supposed to answer only one question that is the first one. For the…

Q: QUESTION 6 Find the volume of the solid generated by revolving the region bounded by the given lines…

A: The given curves are y=9x and y=-x+10.

Q: x' + y' – x = cos(t);x' + 2y' = 0; x(0) = y(u) = 0

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Q: [3 2 A = 26 find the general solution of 4 y' = Aỹ + g, g = =

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Q: find ĕ = 1tiG residues Re12) Satis fies the equation

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Q: find residue

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Q: Sumi Kato's savings account has a balance of $1292. After 12 years what will the amount of interest…

A: Compound interest formula

Q: (Fourier series) (a) Show that the pointwise convergent series 00 sin(nx) n1/2 11=1 cannot converge…

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Q: 4 For what value(s) of x is the function f(x) 2x? - 6х NOT continuous? A. x = 0 and x = 3 B. x = 3…

A: To find- For what value(s) of x is the function fx = 42x2 - 6x NOT continuous? x = 0 and x = 3 x =…