What is the nature of the roots of 3y"+15y+33? What is the nature of the roots of 4y"-12y+16?

Q: If |a| <1, the indefinite integral zp- 1+z14 can be written as a power series , Cna14n 13 + C, m31 w...

A: The complete solution is in given below

Q: Find the center, length of major and minor axis for ellipse 4x +9y + 24x = 0 Hence, sketch the ellip...

A: Solutions 

Q: ing False-Position Method, find the Root of the following equation: - 3. x = 0 for the interval (0.5...

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Q: 3. Consider the following system of linear equations: x + 2y – z = -1 2.x + 2y + z = 1 3x + 5y – 2z ...

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Q: Show that the column vectors of following matrix A are linerly independent

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The order of a ma...

Q: 3. Find the area of the region bounded by x = 3 – y and the line y = x - 1. Sketch the graph of the ...

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Q: d. Carlo comes to the party if David doesn't come, but if David comes, then Bruno doesn' come. e. An...

A: The main objective is to express the statements into logical symbols.

Q: 2 In x 1 e* 2 2. 1 In 2x -1

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Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

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Q: A zero coupon bond is a bond that is sold now at a discount and will pay its face value when it matu...

A: Given that: Face value of the bond = $15000 Mature time = 28 years  Buy price = $6000 To determine...

Q: Exercise 3.2.8. (Used in Example 4.6.1.] Let ICR be an open interval, let c € I and let f: 1– {c} → ...

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Q: Make a membership tables to establish each of the following: А. АnВ3 AUB (AnB)U(Anc)=(AnB) (anc) В.

A: We have to prove the given following statement using membership tables,   A)  A∩B  = A ∪ B B)  (A∩B)...

Q: Let f(x) = 1+ + x² + x³ + x4 +x5. Find the remainder R3(x) = f(x) – T3(x). Find the maximum value of...

A: Given:Let f(x) = 1+x+x2+x3+x4+x5  

Q: 12. Use the method of cylindrical shell to determine the volume of the solid obtained by rotating th...

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Q: given differential equation. Use reduction of order or formula (5) in Section 4.2, e-SP(x) dx (5) xp...

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Q: dy - y = e*y? dx

A: Let us consider the differential equation of the form dydx+Py=Q(x)yn It is known as Bernoulli's equa...

Q: 4x +3x3 - 4 Find the horizontal asymptote of f(x) 2x3 + x2 y =

A: The given function is f(x)=4x+3x3-42x3+x2-5 rewrite as  f(x)=3x3+4x-42x3+x2-5 here the degree of num...

Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

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Q: (a) It, for f: AC R + R, at Xo, Ak > 0 for k odd, or Ag < 0 for k even, then show that f cannot have...

A: Local minimum is also known as relative minimum. A function f has local minimum at a  particular poi...

Q: If y, and y, are linearly independent solutions of ty" +2y + te"y = 0 and if W(y, y2)(1) = 2, find W...

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Q: 2. Find the inverse Laplace Transform of the following left-sided signals a. X(s)=+2s +3 6s² + 22s+1...

A: To find the inverse Laplace transform of a)X(s)=s2+2s+3s3b)X(s)=6s2+22s+18s3+6s2+11s+6c)X(s)=3s2+10s...

Q: If T : R^3 -> R3 is a linear transformation defined as T(x, y, z) = (x + 2y, y + 4z, x + 3y + 4z), f...

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Q: Using ɛ-d argument, prove that f(x) = x-[x] is continuous at all x ERexcept the integers. (Note: [x]...

A: Solution:-

Q: Q1: Find the values for (X, Y, Z) for the following equations : X+ 4Y – Z = -5 - (1) 3X + 3Y – 18Z =...

A: The system of equation is ,    x + 4y - z = -5 .........(1)                                    3x + ...

Q: 10 Express the given complex number in rectangular form 1+/3 Answer: a. b. --V d.

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Q: Problem (1): Show that there is only one automorphism, the identity function, of Q.

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Q: What type of symmetry can be observed in the given image? Select the correct response: O Spherical O...

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Q: 8x²y" + 10xy' – (1+ x)y = 0

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Q: Find the three cube roots of the following complex number: 120 ( cos60 + i sin60) O (4.63 + 1.69i), ...

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Q: Suppose that the tringle inequality is strict llel veetor s that means para V Qe R on non get 11 x+y...

A: Given: The triangle inequality is strict on non-parallel vectors, which means that, if x≠αy and y≠αx...

Q: X1 + X2 – X3 = –-3 6x1 + 2x2 + 2x3 = 2 -3x, + 4x, + x3 =1 %3D

A: Given system is  x1+x2-x3=-36x1+2x2+2x3=2-3x1+4x2+x3=1 1: Simple Gauss elimination: We can write it ...

Q: Using a proof by contradiction and the well-ordering property, prove Vr E R, if 2 < r, then Vn E N, ...

A: Every nonempty subset of natural numbers has a smallest element, i.e, if B is a nonempty subset of N...

Q: Tnis symmetry is characterised by the ablity to draw an enaless, or great but finite, number of symm...

A: According to the given definition, this symmetry is characterized by the ability to draw an endless,...

Q: 20. Prove that an angle of 0 radians is constructible if and only if the real number cose(sine) cons...

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: Bessel’s function Prove that J2'(x)=(1-4/x2)J1(x)+J0(x)

A: According to me you have asked misprinted question. Please see the correct proof of this question. ...

Q: 2z Use method of partial fractions to find the Inverse Z-transform of 22-1 IzI >1

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Q: Find all the cube roots of 1 - i , i.e., (1 - i) ^1/3 .

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Q: (a) Determine the appropriate Green's function by using the method of variation of parameters for th...

A: Green's Function: The Green’s function approach is particularly better to solve boundary-value probl...

Q: Solution by Jacobi's Iteration,

A: Note:- As per our guidelines, we can answer the first part and first method of this problem as both ...

Q: Determine the amplitude, period and displacement for the given function, and sketch the graph of the...

A: y=2.5 cos2x+π6    

Q: Find the singular integral of z = px + qy + p/q

A: Complete integral

Q: Given the trapezoid below find the measure of GH.

A: Given,        

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Q: e3z I dz (ez + e 5z )2 II

A: Introduction: The Ortrogradsky's method is used in finding integration when the integrand is a ratio...

Q: Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)=f(x) f(y) ¥x, yER. Show th...

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Q: diffrentfal Equatton 2c05(5t+ 1•0472) UL4) %3D %3D where ultl Unut stop funchion finell the compleme...

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Q: Use De Moivre’s Theorem to find the identity of the following:

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Q: Using Newton- Raphson method, Determine the points of intersection between the circle x +y = 3 and t...

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Q: 3. Using the substitution z = xy, convert dy x+y = 2x V(1 – x²y²) dx to separable equation. Hence, s...

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Q: Using Theorem 3, find f(t) if L(F) equals: s + 10 ? – s – 2

A: We have , Lf(t) = s + 10s2 - s - 2 We need to find Inverse Laplace Transform , i.e. f(t), Here , F(s...