use Newton’s Method to find the root of the given equation, accurate to six decimal places, that lies in the given interval.

Q: Find the centroid of the solid bounded by x² = 4y and y = 5x - x² about the x-axis.

A: We will draw the region and rotate it about x-axis to create a solid of revolution . We will need…

Q: 4. Find the Fourier Series of the given periodic function. 4, f(t) = {_1 -π≤ t ≤0 0 < t < π

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Q: 5 2 d. L−¹³+; 3s-5 5s-4 e. L- L-¹1- 2s²-3¹ 1 f. L-11 s2-8s+25' 7s

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Q: Evaluate. [ 10.xªtan (2x³ + 3) dx

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Q: d²y 5. Consider the differential equation dy 6- +9y = 9x + 3. dx dx² (a) Find the general solution.…

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Q: Use the given information to decide which lines are parallel. Justify your answers with a theorem or…

A: Fact (1) converse of parallel line theorem  The converse of the theorem is true as well. If two…

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: Given z=ex2+y2, x2+y2=1, x2+y2=9, z=0

Q: y (0) 6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the…

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Q: Compute the Fourier series for the given function ? on the specified interval.

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Q: (a) Use the method of Lagrange multipliers to determine the minimum and maxi values of f(x, y) = x²…

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Q: Numerical Differentiation: f(x) = e² 1. COS X -2 Find f(1.5) and step size of h=0.75 and 0.1

A: We will use Forward Differentiation formula f'(x) = {f(x+h) - f(x)}/h  to find the value of f'(1.5)…

Q: S. (22² 2. 2 (2x² – 3x) dx

A: ∫25 2x2-3x Apply the Sum Rule:    ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx =∫252x2dx-∫253xdx

Q: Simpson's Three-Eighths (Use n = 12) 9. So¹ (3x²+3) dx 10. (2 sin x + 3cos 2x) dx

A: First we find general solutions: 9.  ∫13x2+3dx=∫13(x2+1)dx=13∫1(x2+1)dx=13tan-1x +c    then…

Q: (b) Pak Majid sells three grades of eggs A, B and C. The total price of a grade A egg and a grade B…

A: We have to solve for the values x,y, and z by using the inverse matrix method.

Q: the following matrix orth APT is diagonal.

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Q: (20pts) For the function f(x, y) = -xy2, find the solution from x = 0 to x = 1 with an increment of…

A: Solution: Given , y′=-xy2y(0)=1h=0.2 Forth order R-K method 1st iteration :…

Q: Find the Fourier transform of the given waveform. f(t) -2 -1 1 0 1 2 (s)

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Q: 10 Estimate ¹0 f(x) dx from the following table, using Simpson's Rule. X 0 1 2 3 4 5 6 7 8 9 f(x) 40…

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Q: Find the z-transform of the following equations: b. cos(3n) + 2 sin(3n)

A: We need to find z - transform of , un = cos3n + 2 sin3n That is , zun = zcos3n + 2 sin3n zun =…

Q: 4. Let Z5 = {0,1,2,3,4}. 4a) Find the value of x that makes (2+5) X5 4 =_1 in Z5 true. Complete the…

A: Given :  ℤ5 = 0, 1, 2, 3, 4. To find : (i) The value of x in  ℤ5  that satisfies  (2 +5 x) ×5 4 = 1.…

Q: a) Find a closed form of the solution using the method of Taylor series about x = 0. b) Use Euler's…

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Q: on 3. Let f(x) = |x| Compute f(n) for all

A: Given:  f(x)=x x∈-π,π. To find: a) f(n) for all n∈ℤ.              b) ∑n=1∞12n+14 and  ∑n=1∞1n4

Q: B/Find the oblique asymptote of the function f(x) = -3x²+2 x-1

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Q: 1. 3. Determine [[e=²*² +25-+²] kt [[e+cos (√2+)] [[ext_H(t-a)]

A: Used Formulae :  L{eat} = 1/(s-a)  L{1} = 1/s L{tn} = n!/sn+1  Shifting theorem of laplace transform…

Q: a²z Find of z= In(xy) a²y

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: What should be the base number “N” to make the equation 5N/44N = (0.121212…)N true? A. 17 B. 15 C.…

A: The decimal number system uses 10 as the base. In the decimal number system, the place value of each…

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A: Given Fourier transform of the function ft with respect to t Fft=∫-∞∞ft e-iωt dt Fω=∫-∞∞ft e-iωt dt…

Q: a b c.....there are 3 sub parts that you need to solve

A: As per the question we are given a recurrence relation in xn and we have to find : Generating…

Q: (a) Find the mass, M, of a solid sphere with radius r = 2 and density function given by f(r.o) = ² =…

A: A solid sphere with radius r=2 and density function given by…

Q: Numerical Integration: c2 1 S Jo √x 1. =dx

A: We will first solve the given integral directly and then apply numerical integration. Consider:…

Q: Find the Fourier transform of the given waveform. f(t) -2 -1 7 1 0 1 2 r(s)

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Q: Show that matrix multiplication is associative i.e. A(BC) = (AB)C when- ever the multiplication is…

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Q: Find the Fourier transform of the given function. 2A f(t)==t+ A, St≤ 0; T 2A f(t)=== Ft+A, T f(t) =…

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Q: 3. Using the Gauss-Seidel method make three iterations for the linear system x(0) = 0, 4x - y -z =…

A: Solution :-

Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: Follow up question. We are given   α2 = 0.1[cm2/s] and a hoselength of 1m. What is the temperature…

A: As per the question we are given : α2 = 0.1 cm2/s, and the hose length : L = 1 m Now using the…

Q: 2. The Minimum point of y = 8x+4 (x-2)²

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Q: Formula valid for matrices? explain why? (A + B)(A - B) = A²B²

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We will sketch the region and also find boundary curve .Then convert every equation into polar curve…

Q: Estimate the integral 6.8 [..* ƒ(x) dx using the best combination of the trapezoidal rules, Simpson…

A: For x=0 to x=0.9 we apply Simpson 3/8 rule For x=1.7 to x=3.1 we apply trapezoidal rule For x=3.8 to…

Q: Find the eigenvalues of the following matrix, Z: 1 -1 01 Z = M 2 -2 1 NJ For this question, you are…

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Q: Please provide a step-by-step and clear solution to each of the problems below. 1) Parabolic…

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Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

A: Solution

Q: Show full solution: Find all relative extrema and saddle points of the following function using…

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Q: and conversely.

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Q: 3. Solve the following differential equations using Laplace transforms: 1 dx d²x dx +4 dt² dt +4x=t²…

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Q: Find 3²y of z = In(xy)

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Q: 16 Tandem Cycling Triplets Peter, Reeta and Nikita have two ways for getting home from either one or…

A: Since you have asked a question with multiple subparts here, we will solve the first three sub parts…

Q: 8. Given vector v = (4,-5) a) If we want to represent v in the form v= AB where A = (-2, -3), what…

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Q: Create a quadratic model for the data shown in the table 1 -1 X Y -1 -1 Oy=0.85x² +0.11 - 1.78…

A: