Let a, b, c be real numbers. If ax' + bx +c = 0 has two real roots a, B where a <-1 and B >1, then show that 1++4| <0.

Q: Utt = 8uxx for 0 < x < ™ u(x, 0) = x² u(x, 0) = 1/2cos(8x) Uz(0, t) = u„(T, t) = 0 %3D II

A: The given P.D.E is                            utt=8uxx for…

Q: 5. (i) Let A be an nxn matrix over C. Show that the eigenvectors corresponding to distinct…

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Q: erentiation and/or integration to express the following function as a power series (centered at æ =…

A: In this question, the concept of power series is applied. Power Series A series of the form ∑n=0∞…

Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y = eV guaranteed by…

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Q: 1 2 3 4 4321 (b) 21 4 3 (c) -2 3 41 2 -3 -2 10-2

A: Determinant is 4

Q: If f is a field containing an in finte humber of destinct of distinst elen

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Q: Q2: Find a root of x- 0.5 – 2-2x = 0 by using Newton-Raphson method correct to %3D 4 decimals so…

A: x-0.5-2-2x=0⇒f(x)=x-0.5-122x⇒f'(x)=1+2ln(2)22x Taking initial guess x0=0 Newton-Raphson method:…

Q: and ind scalars a and b such thai Dw.

A: given u=8i+4jv=i+jw=i-jWe have to find scalar a,b Such that u=av+bw

Q: • Consider the fiunction g defined by glx, y)> cos (7x y)+ logs (x-y) la) determine dydx

A: The function in the form z=g(x,y) is called a multivariable function. The output of the function…

Q: Prove that Sn is true for all natural numbern 1 1 1 1.2 2.3 3.4 n(n + 1) (n + 1)

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Q: dz IV. Suppose z is a function of æ and y, and a? – y? = 2"e®y. Solve for dx

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Q: У" - бу + 5у %3DЗе *; у (0) — 2; у'(0) — 3

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Q: 6) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Review Exercises for Chapter 2, #…

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Q: nsider the equation of the surface S given by 2x. + 3XYP + y2 wher mber and ß is an impair number ,…

A: In this question, the concept of the derivative is applied to find out the tangent to the plane.…

Q: 1. (i) Show that if A is an n x m matrix and if B is an m x n matrix, then A 0 is an eigenvalue of…

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Q: , How many ways are there to distribute r+s identical balls among five different children such that…

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Q: Determine whether the Fourier series of the following functions converges uniformly or not. Sketch…

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Q: Consider the product of cycles (1 2)(4 7 8)(2 1)(7 2 8 1 5) that are permutations of {1, 2, 3, 4, 5,…

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Q: Q2: Find a root of x - 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that…

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Q: 3 If X 1 - the value'of X" is 1 3n - 4n (a) 2 + n 5-n (b) - n | 3" (- 4)" (c) (d) None of these 1"…

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Q: 2) Consider the fiunction g defined by (TX/y)+ glx, y) = COS log3 (x-y) la) determine dydx

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Q: Q8. Determine u(0.4), using the fourth order Runge-Kutta method, given that u = , u(0) : = 1.…

A: The absolute error is the difference is the exact value and the approximate value.  The relative…

Q: 3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a)…

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Q: 2= 12 mod 2 - - 2 = 11 mod 18 20 = -2 mod 19 - 2= 20 mod 2 - -17 = 20 mod 8 6.7 = -14 mod 11 - -1 =…

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Q: The Cookie Jar bakes 80 dozen cookies at a cost of $1.08 per dozen. If a markup of 60% on selling…

A: Introduction: The cost value of a piece is that the quantity spent to get it or the value at that…

Q: 1. Given the vector u = (2,0, 1). (a) Solve for the value of a so that u and i = (a, 2, a) form a…

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Q: 4 Find the arc length of y = (**)' + over [1,2]. 2(x+5)? (Use symbolic notation and fractions where…

A: Arc length of the curve

Q: Problem Consider the 2n x 2n matrix On -In On InER2nx2n J := A matrix SE R²n×2n is called a…

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Q: Let R=Z and R'= set of all even integers. Then %3D (R', +, *) is a ring, where a*b = ab V a, be R'.…

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Q: matrices over K. For each j, 1 <j<n, the function E defined by

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Q: Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES: y co) = し h=o.2…

A: Given the ODE y'+5x4y2=0 and  y0=1⇒x0=0, y0=1   Step size h=0.2 Solve using Euler's Method at a…

Q: If f(x, y) = y cos(x) – x³ In(y), find the second partial derivative dy dx

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Q: SEGMENT Directions: Solve for x. Clrcles may not be drawn to scale. I. 2. 4 6. 3 5. 4 3.

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Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n

Q: Estimate f(7) from the given data using Lagrange's Polyn

A: Given, x -3 1 5 5.3 9 F(x) -9 -3 0 7 15

Q: Approximate the following integral using the Trapezoidal rule: e+1 dx x In x and find a bound for…

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Q: 1. Prove that if f(x) is bounded and measurable on E, and c is any constant, OMNIA then S, [f(x) +…

A: Given, f(x) is bounded and measurable on ETo prove: ∫Ef(x)+c=∫Ef(x) dx+c m(E)

Q: Rotate the region bouNded by X= (y-3)² and x= 16 about the x=-5

A: 1st we will find shaded region bounded by given curve and line

Q: describe the following Feasibility and optimal solution Surplus versus Slack variables Alternative…

A: Solution 1: Feasible solution:  All possible solution, which satisfies the all constraints are…

Q: Test the convergence and divergence of the following series. find the sum of Fonvergent series. 2)…

A: Here we have to test the convergence and divergence of given series.

Q: Let Ean, Ecn, and Ed, be series with THEOREM 10–The Comparison Test nonnegative terms. Suppose that…

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Q: . Let R be the ring of all complex numbers and R' the a b b a ring of all 2 x 2 matrices of the form…

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Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan I - 3y + 2z = 18 %3D 5x -…

A: Since there are two equations and 3 unknown i.e. 2 Rows and 4 columns but For the method to solve…

Q: A line passes through the points P(9,5, – 1) and Q(- 9, – 3, – 8). Find the standard parametric…

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Q: 2.3 Consider the nonlinear system 1 i = y + x (x2 + y2 –- 1) sin x2 + y2 – 1 1 y = -x+ y (x2 + y2 –…

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Q: Solve

A: We use Mathematical Induction method to prove given example.

Q: iven: surface Q : 9x² – 4z² = 9y a) Give the equation of the trace of Q on each coordinate plane and…

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Q: For the sequence defined by: a1 3D3 3 An+1 - an Find: a2 a3 %3D a4 II II

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Q: Verify the conditions that must oply in order to use the integral test for the eries E, n'e. ( Using…

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Q: Minimize: Z = x + 3y Subject to: x + 2y > 6 х — у <3 X, y 2 0

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