QUESTION 7 (i) -2+ (iv) 2.31 The constant a is such that ["xe*dx = 6. (1i) Show that a satisfies the equation x = 2+e. (i) By sketching a suitable pair of graphs, show that this equation has only one root. (iii) Verify by calculation that this root lies between 2 and 2.5. (iv) Use an iterative formula based on the equation in part (i) to calculate the value of a correct to 2 decimal places. Give the result of each iteration to 4 decimal places.

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Q: Question 18 ▼ Two cars are moving towards an intersection. One car is 150 meters north of the…

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A: We have to find how fast ladder sliding across the floor .

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A: Given that  The limit is

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A: Given - x'' + x' + 3tx3 = 2et , x0 = 1, x'0 = 4, ∆t = 0.2 To find - Use the Euler method with a time…

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A: Newton Raphson method

Q: Question 2: a) find the value of 'a' in order that f(x) = v3 sinx – cosx – 2ax +b decreases for all…

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Q: Question 1 Select the formula that is used for Newton's method. f(zn-1) f(tn-1) Tn = In-1 + f(zn-1)…

A: The formulae that is used for newtons method isxn=xn-1-f(xn-1)f'(xn-1)

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A: Given, Leaking out rate from the inverted conical tank is 9200 cm3/min height of tank is h=6 m,…

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Q: Question 2 * SE sec2 (0) d0 = dx a) sec² (x³) - 3x² b) – sec² (x³) · 3x? | O ) sec² (x³ ) d) – sec²…

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

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Q: 14 The number of foxes in a state park is recorded in the given graph. The number of foxes was at a…

A: Given ,  function f(0)=150f(6)=60 now satisfy from given equations, f(x)=50cosπ6x+100 at x=0…

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Q: * = x- y², y(0)=1, with step size Ax = 0.25 over the interval 0<x< 2. dx

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Q: 1-2 -1 2 3 1 b-a 2 1 4 E -Cos²x sin 2x 1 -2 - e b+ a e 3-b - 1 2 o 2 -1 O 1 -1 2 e 1 943 O 3 1…

A: Matrix addition is possible if the order of the matrices is same  Matrix subtraction is possible if…

Q: Question 5 The first approximation(p,) of the root of the equation f(x) = x° – 2x² – 2=0 by Newton…

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Q: a 0.9062 Cos (1-√3x) dx = 1/2/2 : -0-1 a=0.5968

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Q: Question 12 of 16 > Find the equation of the tangent line to f(x) = 10e* cos2(x) at x 4 (Use…

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A: 6. Let  pth root of a number be x=N1/p. Newton Raphson formula finding the root.…

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Q: cos (1/x) dx ∞ o COS 21. 12

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Q: Question 18 > Two cars are moving towards an intersection. One car is 170 meters north of the…

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Q: Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 2…

A: Given:    East = 3  mi/h    Northeast = 2 mi/h   Time = 15 min = 0.25 hr

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Q: Question Let x34x 1 0. Determine the root to which Newton's Method converges for the initial choice…

A: We know,