Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x 1+ x²

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) dx finel

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Q: The Newton Raphson method is also called as O a. Secant b. Tangent method

A: Newton-Raphson Method: The Newton-Raphson method  is a way to find a good approximation for the root…

Q: Find Equatien of the tavgnt lin tu th cuve at tk giver pointe y= sec X ,

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Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the length of the arc y = In(cos x) between the points (0, 0) and (pi/3, -In2).

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Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

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Q: Use the trapezoidal rule with n = 5 to approximate 3 cos(x) -dx Keep at least 2 decimal places…

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Q: .Find the estimate for the root of f(x) = sin x + cos (x² + 1) – 1using Bisection methodx, = 1. 5,…

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Q: Let f(x) = x³/2. Determine the length of the arc swept over x E la, b).

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Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

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Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: x3 V4 + x2 dx

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Q: Derive the third order dervitive formula at x = x, by using Newton's forward differences

A: Consider the function y=fx which is tabulated for the values xi=x0+ih, i=0,1,2,.....,n. Suppose that…

Q: Find the Residues of given points 1 at z = nt sin z

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Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: 2 Find the arc length for y = 3x3 on [1, 8]

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Q: a²z a2z If z = arctan (2), find ду?

A: It is given that z=arctanyx z=tan-1yx

Q: • Use the trapezoidal rule with n = 14 to estimate: -dx √√1+x²

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Q: Find the smallest positive root by using the bisection method f(x) = 4 cos(2.x) –-x' +5 with 3…

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Q: Derive the third order dervitive formula at x = x, by using Newton's forward differences.

A: To find dydx, differentiate the Newton's forward difference interpolation formula with respect to p,…

Q: Use the trapezoidal rule withn= 20 subintervals to evaluate I = 1 = f; sin²(VRr) dx.

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Q: Use Simpson's rule with n = 6 to approximate %3D cos(a) dx 0.08 Keep at least 2 decimal places…

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Q: cos(x) dx

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Q: sketch, eva luate freverse integ ration order of 2. 2. 4-X 2y e dy dx 4

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Q: 4. Find the length of the arc C = {(x, y): y = V16 – x²?,0 < x < 3}.

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Q: . Find the polynominal of degree 9 centered at 0 that best approximates f(x) =ln(x3+5) b. Now use…

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Q: Let f(x) = x3/2. Determine the length of the arc swept over r E (a, b).

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Q: By using Trapezoidal rule, the value of “h" in evaluating (x² – 2x + 6)dx , by taking 10…

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Q: While evaluating approximate value of 7 | x² dx, using Trapezoidal rule, taking 4. n = 10, the value…

A: The given integral is ∫47x2 dx. Compare the above integral with its standard form ∫abfx dx and…

Q: Use Simpson's rule with n = 6 to approximate cos(x) rp-

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Q: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

Q: 2. Approximate the sol of x = sinx upto 4 decimal places by using Newtons method. Eind th ainta find

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Q: .Find the estimate for the root of f(x) = sin x+ cos (r+1)-1using Bisection methodx, = 1.5, X=2 with…

A: Solution

Q: Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975…

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Q: Use Gaussian Quadrature of order 5 to approximate 08 6 2 x-1 To how many decimal places is this…

A: Given that,    f(x)=∫286x-1dx                                  1 Using the Numerical Integral by…

Q: Q: Prove that the arc lenfth af Curve y = log secx from to n- 3 is Use formula Note I+ ( dn.

A: Given: y = log sec x To prove: The arc length of the function y from x = 0 to is .

Q: Given f(x) = sin x + cos(1 + x^2) − 1 in a Bisection Method with initial estimates of 1.5 and  2.5,…

A: Here I run a python script to calculate that value. You can easily print intermediate steps in that…

Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

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Q: To evaluate f dx, the integrand can be transformed to 1-sin?x

A: Follow the procedure given below

Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

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Q: I* cos z lim 1³+2

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Q: Use the trapezoidal rule with n = 4 to approximate cos(x) de Keep at least 2 decimal places accuracy…

A: Given that: ∫14cosxxdx and n=4

Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

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Q: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: Use the trapezoidal rule with n = 20 subintervals to evaluate I = -5 sin² (√0× t) dt

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