Let g(s) = (282)7. Then g'(s) is g'(2) is g" (s) is and g' (2) is "

Q: 12. Let xo < x < < x, and let f be continuously differentiable. Show that a f[xo, x₁, x₂] = f[xo,…

A: A continuously differentiable function has a derivative at every point, and that derivative is…

Q: x (t) = 2sen (nt) + 3sen (nt) + 4sen (nt)

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Q: If q(x) is an arbitrary polynomial in Pn it follows that                                      q(x) =…

A: Given, if q(x) is an arbitrary polynomial in Pn it follows that                   q(x) = c0p0(x) + .…

Q: as Calculate (x sin y + e). ax²əy³

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Q: 1 if g is the inverse of function f and f(x) = 1+x? prove that g'(x)=1+{g(x)}"

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Q: Prove that Σan σ(d) φ (n/d) nτ (n) and ΣIn τ(α)φ(n/d) σ(n). ||

A: As per the question we are given two sum identities including the Dirichlet convolution :…

Q: 4. Define Let T: M2x2 (R) → P2(R) by T (a b) = (a + b) + (2d) x + ba². c d B = {69). C )·(9)· (9)}…

A: We will find the matrix with respect to the basis.

Q: [1 1 1 1 3 1 3 1 2 2 2 2 *|-jx7.558 1 3 1 1 3. 2 2 2 2

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Q: [X1 X2 4) If A X3 [x4. 1 find all the unknowns using Cramer's rule. |0 -1 -2 -3 -41 1 Let A = 3 6 5…

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Q: Let C = {0, 1, 2, 3} and f: C → C, g: C → C with ƒ = {(0, 2), (1, 2), (2, 3), (3, 0)}, {(0, 3), (1,…

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Q: (x- 1) (x– 2)(x+ 1) (x+ 2)(x- 3) (x+ 3) 2. Let f"(x) = and g'(x) = For what values of x are Az) and…

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Q: 3) a) Determine the linear Lagrange interpolation polynomial that passes through the points (-1, 2)…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Let f(x) E R[x]. If a + bi is a complex zero of f(x) (here i = V-1), show that a – bi is a zero of…

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Q: Which of the following functions from R to R are one-to-one, which are onto, and which have inverse…

A: For a function to be one-to-one, each output value must correspond to exactly one input value. The…

Q: Which of the following is the inverse of the functionf : [0, ∞) → [3, 0), f(x) = 2.x² + 3? Select…

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Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: The algebra of differential operators closely resembles the algebra of ordinary real polynomials.…

A: True

Q: Simplify the given expressions using the postulates and theorems of Boolean Algebra. a. F = xy + xy'…

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Q: f(x) = y= Find the domain and the ring x 2 x+2 x² 2 3 / /

A: What is Domain and Range of a Function: A function always maps two sets. Either the two sets are…

Q: Prove n k>0 () = n2n-1

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Q: 3. There are three distinct cube roots of any nonzero real number c. (a) Set up an algebraic…

A: Sol:- (a) To find the three distinct cube roots of a nonzero real number c, we can set up the…

Q: 3. The left shift operator is given by T : l² → l² by T(x1, x2, x3, ....) := (x2, x3, x4, ....) for…

A: To find the operator norm ||T || of the left shift operator T : ℓ2→ℓ2, we need to find the supremum…

Q: (5) Compute -2 67 using Euler's criterion.

A: Objective: To compute -267. Concept used: Euler's criterion, is a result from number theory that…

Q: Prove the general formula φ(gcd(a, b))φ(ab) = gcd(a, b)φ(a)φ(b).

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Q: 2) Find the complex Founer senes of a 2c - periodic function f, which is defined as f(x)= (ix-1)² in…

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Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: ons 1-e2z (b) 3.

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Q: Use of Cramer's Rule 2x, – 3x, = 5 X +x, = 5 [1 1][x, X

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Q: Find the value of f(0) when f'(t) = 3 sin(2t), ƒ(7) = −1. 1. f(0) 2. ƒ(0) 3. f(0) 4. f(0) 5. f(0) =…

A: f'(t)=3sin(2t)we know ∫sintdt=-cost+c

Q: A function f is even if f(x) = f(-x) and odd if f(x) = -f(-x). For example, f is even if f(x) = x2…

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Q: (d) Determine the right cosets of ((1 2), [1]) € S3 x Z2.

A: I just used the definition  of cosets

Q: Find limn→∞ Zn, where zn = 2n + 2 n + 2n 2n +1 -i.

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Q: 4. Consider f(x) = sinr. If f(x) is interpolated by p2(2) polynomial with the nodes {-7.0, }, the…

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Q: Example: Show that the function Az) = z² is analytic. z = x+iy S(2) = z

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Q: Prove the general formula φ(gcd(a, b))φ(ab) = gcd(a, b)φ(a)φ(b)

A: Prove the general formula: .