Prove the following: If (xn) converges to x, if x 0, and if rn 0 for all n 2 1, then there Prove that the sequence (n)1 where xn = (1+)" is monotone increasing and

Q: Find the derivatives of y with respect to x: a) y = xe* - e* b) y = e(1x+) %D c) y = e*(sin x + cos ...

A: (a) The product rule of differentiation is as follows: uv'=u'v+v'u The required differentiation form...

Q: The 2nd approximation to the real root of the equation e - 4x = 0 with initial guess xo = 0.3 using ...

A: Newtown Raphson method

Q: Find the Fourier series of f (t) = t³ where t e [-4,4] and f(t + 8) = f(t).

A: Given function, f(t) = t3 where t∈-4,4 we have f(-t) = (-t)3 = -t3 = -f(t)So f(t) is an odd function...

Q: Q1) The growth rate of a certain strain of bacteria is unknown, but assumed to be proportional to th...

A: The exponential growth or decay is modelled using the formula: Nt=N0ekt, where N(t) is the populatio...

Q: (c) Let I = (f(x)) be the principal ideal generated by f(x) in Z2[r]. Calculate the multi- plicative...

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Q: sin z What kind of discontinuities have the functions y = cos z and ? at x = 0? Indicate the charact...

A: ka

Q: (1) If A is nx n, then A and A have the same eigenvalues. (ii) If A is nx n, then A and A have the s...

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Q: $7/4 -t -31/4 -T/2 /4 T/4 T/2 3/4 57/- -2 -4 -5 of Identify the function whose graph appears above a...

A: The tangent function is one of the three basic trigonometric functions. Its reciprocal is he cotange...

Q: Problem 8. Determine all 2x2 matrices A with the property that AB = BA, for every 2x2 ma- trix B.

A: We have to find type of matrix A which will satisfy AB=BA 

Q: Let U be the subspace of R' spanned by {u1, u2, u3}, where иј 3 (1,1, 1, 1), из — (1,—1, 2, 2), из —...

A: Use the Gram-Schmidt algorithm.

Q: 1. d = 9in VOLIME (INTRIS O F) VOLUME(DEARST TENT)

A: The volume of a sphere is V=43πr3, where r is the radius of the sphere. The radius is half of the di...

Q: The region inside both of the circle r = 2 sin 0 and r =1. Which of the following gives the area of ...

A: Let us consider the double integartion ∫R∫f(r,θ) drdθ where R is the region of integartion in the po...

Q: II Answer the questions below about the quadratic function. g (x) = 3x – 12x+16 %3D Does the functio...

A: Introduction: The extremum of a function can be calculated by using differentiation. This is the imp...

Q: 3. (p + r) v (9 → r) = (p a q)

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...

Q: 8) Which of these pairs are equal? A) sin 49° and sin 51° C) cos 28° and sin 72°

A: Some of the properties of the trigonometric sinπ-θ=sinθ cos(2π+θ)=cosθ cos(2π-θ)=cosθ cosπ2-θ=sinθ ...

Q: A hole is drilled through the center of a sphere x² + y² + z = R,², leaving a ring-shape solid. If t...

A: given sphere x2+y2+z2=R2s and a ring shaped solid is of cylinderical shape x2+y2=R2d use of polar co...

Q: The 2nd approximation to the real root of the equation ex – 4x = 0 with initial guess xo = 0.3 using...

A:

Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1, 1,0,0...

A: To find- Find an orthonormal basis for W⊥, where W is the subspace of ℝ4 spanned by the vectors -1, ...

Q: (1) Let G be a group of order 94 = 2 x 47. Let Z(G), as usual, denote the center of G. (a) For each ...

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Q: Let a > 0 and let f: [0, a] –→ R be an increasing continuous function. Consider the curve C parametr...

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Q: Graph the following functions. Create a table for the range. Use the domain (x) = {-2, -1, 0, 1, 2} ...

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Q: 1. The function f(x) is given in the following tabulated form. Compute [1f(x)dx with h= 0.3 and with...

A: Given:  x 0 0.3 0.6 0.9 1.2 1.5 1.8 f(x) 0.5 0.6 0.8 1.3 2 3.2 4.8 To find: ∫01.8f(x) dx wit...

Q: Which adjacency matrix represents graph G? b d e G го 1 0 1 1 0 0 0 1 a 1 1 1 1 1 1 0- ro 1 0 01 1 1...

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Q: Find the shortest path in the graph from s to y. 6 2 1 8 3 5 H No answer provided a. S, z, y b. 5, z...

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Q: 3 -1 8 1 |-6 4 -3 D = 10 4. Decompose matrix D.

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Q: Consider the following Differential Equation (Riccati Equation): y' = p(x) + q(x)y+r(x)y² If u is a ...

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Q: Evaluate e21.1.png aln(v) dx using Trapezoidal Rule with 8 equal intervals. if a = 14.49, b = 2, and...

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Q: 2. Find the modulus and argument of 5 – 7i.

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Q: Using Cauchy-Riemann equations, show that the function f (2) = (z+8)² is differentiable everywhere.

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Q: а. Determine the discontinuities of the following functions and state why the function fails to be c...

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Q: ind the general solution: 9y''(x)  + 12y'(x) + 32y(x) = x +ex

A: We are given non homogeneous linear differential equation first we will form the general solution us...

Q: Choose the best definition of arc length. The angle made by taking the radius and wrapping it round ...

A: Arc length of the curve

Q: volume of the follwing object - image attqched

A: Introduction: The formula of the total surface area is given by, T.A.=h (b + d) + l (a + b + c + d) ...

Q: ose wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the...

A: Given the dimensions of the rectangular prism as: 6 meter, 15 meter, 6 meter, 8 meter, 6 meter, and ...

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e

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Q: 5.6 Locate the first nontrivial root of sin(x) =x² where x is in radians. Use a graphical technique ...

A: Given that sin(x)=x2 Let f(x)=sin(x)-x2 Graph of given function is In the figure,  we see that grap...

Q: Which adjacency matrix represents graph G? b d e G No answer provided го 1 1 0 01 10 1 1 0 |1 1 0 1 ...

A: Adjacency matrix representation

Q: C. Identify the proper term for each of the following: 5. WUY 6. ZVDY 7. ZVUY

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Q: Find the modulus and argument of 5 - 7i.

A: Since the modulus of a complex number a+ib is |a+ib|=a2+b2. So, the modulus of 5-7i is |5-7i|=52+(-7...

Q: f(x) = V25 %3D 3.

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Q: Determine whether the initial value problem y′ = cos(t + y), y(t_0) = y_0 has a unique solution defi...

A: Suppose, an initial value problem y'=ft,y is provided. If the function ft,y is continuous on a recta...

Q: Floors and ceilings. For all proofs in this question, you may use the following fact Vx E R, 0 < x –...

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Q: Which matrix represents the number of walks of length 2 and how many walks of length 2 are in the gr...

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Q: For the Initial Value Problem given below: dY + 2y = 2 - e¬4t y(0) = 1 dx Use Euler's method with a ...

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Q: Which of the following subsets of R³ are linearly independent? {0} {{} } {O O } S1 S2 S3 6. 2 S4 = 1...

A: To determine which of the following subsets of R3 are linearly independent. S1=112S2=112, 212S3=112,...

Q: Find the solution of y'(x) -ay(x) = 0

A: In this question, the concept of the differential equation is applied. Differential Equation A diffe...

Q: Zoo authorities want to create several large enclosures so the animals can roam freely. Certain anim...

A: Zoo authorities want to create several large enclosures so the animal can roam freely. Certain anima...

Q: What is the volume, in cubic units, of the rectangular box shown below? A 15 100 C 120 148

A: Given figure is which is a cube. Formula for the  volume of he cube is V=length×breadth×height     ...

Q: For a binomial distribution with n = 10 and p = 0.7, what is P(X = 6)?

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Q: Compute the error at the given condition: • 1. y = sin 3x, using h=1, x = 0, until 5th order Taylor'...

A: We'll answer the first question since the exact one was specified. Please submit a new question spec...