Let a, = 1 and a₁ + a1 = n² + 2n, n ≥2. Evaluate S

Q: Consider the following sequences n (i) In (1 + n) (ii) e"/ (n²+1), (iii) √√n²+2n -n. Which of the…

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Q: Consider the function defined by m(x) = ln(1 + x). (a) Determine the Taylor series expansion of m…

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Q: 1. y=x²-1, y=-x+2, x=0, x=1

A: To find the area bounded by each of the given curves :-

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A: Here the given implicit function is                                          x3y2+xy3=2x2 We have to…

Q: The characteristic equation for a 5th degree, homogeneous, constant coefficient DE is p(x)…

A: given characteristic equation p(x)=x3(x2+1)

Q: 13 8 Example 4.4. Using the partition method, find the inverse of A = 6 9 14 6 -1 13 7 5 4 16 26 9 3…

A: Here, we need to use partition method to find inverse of A.

Q: dt² 3.) +4 dt³ d'y dt² + 5 dy -6y=-12 y (0) = 1, y' (0) = 4, y' (0) = -2 ; dt

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Q: Example 2.25. Find a real root of the equation cos x = 3x - 1 correct to three decimal places using…

A: Here, we need to use Iteration method and Aitken's Method to solve given equation.

Q: A closed wood storage having a volume of 27 in.³ is to be in the form of a right-circular cylinder.…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Example 2.34. Apply Muller's method to find the root of the equation cos x = xe which lies between 0…

A: Here we need to use muller's methode.

Q: Find the function y = 2 sin 3X cos 2X dy dx

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Q: (a) fo dx 4√3x-x²

A: According to our guidelines we have to answer the first question if multiple questions are posted.…

Q: Let g (x, y) = 7 sin(xy) — 9x² ln(y) + 8. Find the degree 2 polynomial, p, which best approximates g…

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Q: 2) If tan (0) = -1.48, find cot 1 cot ( 12-0).

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Q: The power series representation of f(x) = ln(x²-1) is given by OA. (-1)" Σ -x+1, -1<x<1. n=1 n+1 B.…

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Q: Transform * y = 3sinh (3t) 3 s² +9 3 s² - 9 OA) O B) Transform * s² + 1 S³ + s OA) OB) 1 - sint 9 s²…

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Q: 1. Given S = 1 8 0 {][]} 2 1 CR³. 0 61 A. Show that S is a basis for R³. B. Apply the Gram-Schmidt…

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Q: Let S be the sphere 2 + y² +2²=9 oriented outwards, an F = (5x, 7z, -3y) Evaluate: (6₂ F. ds. The…

A: let S be the sphere x2+y2+z2=9 oriented outwards and F=5x,7z,-3y evaluate ∫∫SF·dS

Q: The area of a circle varies directly as the square of its radius. A circle of radius 4 cm has an…

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Q: if q = 5 C when t =0 find 20 22 40 SW current (i) when t = 0.5 charge (q) when t = 0.5 A C 0.05 F

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Q: The numerical value of S X -3 9-x² dx will be equal to *******

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Q: Find a power series solution of y" + (1+x²)y = 0

A: We have given a differential equation ,  y'' + 1 + x2 y = 0 Let , y = ∑n=0∞ an xn  be power series…

Q: Example 2.22. Use the method of false position, to find the fourth root of 32 correct to three…

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Q: Answer the question in the image. Given W = {(x,x+1)|x€ R} ≤R². Is O₂² €W? Select one: O Yes O No

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Q: For numbers 15-17 two parts that are 10 ft. apart is y = 46cosh()-25 15. What is the length of the…

A: According to our guidelines, we can only answer the first question. So rest can be reposted.

Q: A function p(x) has the following features: y intercept: y = 0 Vertical asymptote at x = 1 Relative…

A: given information

Q: Find the 10th element of the following arithmetic sequence, counting 7 as the first. 7,11,15,19,...

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Q: 2 -1 2 3 0 1 5 1 -2 03 -2 -4 1 6 7. Check your answer in item 6 using Cofactor expansion. 1

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Q: A thick cable, 60 ft long and weighing 180 lb., hangs from a winch on a crane. Set-up the integral…

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Q: The face of a vertical dam has the shape of an isosceles triangle of altitude 4 m with an upper base…

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Q: Lewis model requires: 2000 ft of framing lumber 6000 cubic feet of concrete $4000 for advertising…

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Q: The radius of convergence of the ser

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Q: Differentiate x²y3 - y2-6x=0 with respect tox. A 3x²y2-2y −6+2ху 3 2х3у2-2y - 6 6-2xy3 3ху2+у В С D…

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Q: Let R be the region bounded by y = 8 sin(2), y = 8(x - 2)², and y = 2z + 6, and containing the point…

A: We will use the basic knowledge of integral calculus and the theory of evaluation of integrals to…

Q: Optimize the following equation Subject to By using Lagrange Optimization Method? y = 2x₁² - 4x₁x₂ +…

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Q: A spherical tank of diameter 6 m is full of water. Set-up the integral for the work done in pumping…

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Q: How many edges does a tree on 9 vertices have?

A: A tree with n vertices has n-1 edges.

Q: (D5 − 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯* + С3e* +C₁e²x cos3x +C5e²x sin3x y = C₁еx +…

A: We have given a differential equation ,  D5 - 3D4 + 8D3 + 16D2 - 9D - 13 y = 0 It's Auxiliary…

Q: The objective function for a linear programming problem is 3x+2y. If x = 20, and y = 20, what is…

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Q: After another gym class you are tasked with putting the 20 identical dodgeballs away into 3 bins.…

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Q: (1) Determine what comes next in the given pattern and provide solution/explanation: -7, 2, 11, 20,…

A: Given pattern, -7,2,11,20,__,__ Firstly compare the first digit is -7 and 2nd digit is 2 This…

Q: Which ONE of the following statements is TRUE? A. The directional derivative as a scalar quantity is…

A: This is a problem of Vector Calculus.

Q: Let A and B be sets and f a function from A to B. Then the following assertions hold: f'is onto if…

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Q: Consider the following sequences n In (1 + n) (ii) e"/ (n²+1); (iii) √√√n²+2n -n. Which of the above…

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Q: Using the ratio test, find the radius of convergence of the power series Round off your answer to…

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Q: (1) Determine what comes next in the given pattern and provide solution/explanation: -7, 2, 11, 20,…

A: We will write the given pattern in the form of a sequence and will find out the corresponding…

Q: 5. m 1, k-8, b=0 Underdamped Overdamped Critically damped Undamped; Natural period a

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Q: Which ONE of the following statements is CORRECT with regards to the sequences of real numbers? OA…

A: The answer of the given question is given blow.

Q: Example 4.16. Using House-holder's method, reduce the following matrix to the tri- 1 diagonal form:…

A: First check  about the symmetricity (A square matrix  A is called symmetric if A=AT) AT=143412321…

Q: Find the remainder when 7305 is divided by 5.

A: We have to find the remainder when 7305 is divided by 5