•4 Estimate the error if S6 (Simpson's rule with n= 6) was used to calculate sin(2 x) dx . a) O lerror < 0.0702 b) O lerror < 0.1404 c) O lerror < 0.010530 d) O error < 0.2106 e) O lerror < 0.03510

Q: Use Simpson's rule with n = 6 to approximate cos(x) d.x Keep at least 2 decimal places accuracy in…

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Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

A: Composite trapezoidal and composite Simpsons 1/3rd rule

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: 1. Approximate | sin(x²) dx with 12 subintervals by Trapezoidal rule. 1 Simpson's - rule. (a) (b) 3…

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Q: 11. Determine the values of n and h required to approximate e2r sin 3x dx to within 10-4. Use a.…

A: I am attaching image so that you understand each and every step.

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error 1…

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Q: 2 Approximate | sin(x²) dx with 12 subintervals by -4 (a) Trapezoidal rule. 1 rule. 3 (b) Simpson's…

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Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: 4 1 -dx using the midpoint rule with three subdivisions to four decimal places. In(x) Approximate…

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Q: Using secant method, detemine a root of sin Vx - x with initial guesses xo = 0.5 and x, = 1…

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Q: 1. Estimate the root of the expression, f(x) = x² – cos x, using: c. Newton's Method using x, = -1…

A: The equation in form f(x)=0 is called a transcendental equation. The solution of the equation is…

Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

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Q: 10 Use Simpson's Rule with n = 8 to approximate f cosx dx. 2

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Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x&gt;0

Q: In estimating cos(5x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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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: 2. Find a root of f(x) = 6 Sin (x)e* + 1 using Newton Raphson Method accurate to 5 decimal places.

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Q: 3 Estimate the error if S10 (Simpson's rule with n = 10) was used to calculate sin(4 x) dx .

A: I=∫03sin4xdx Integrating it- I=-cos4x403=-cos124+cos04=1-cos124=0.0054

Q: Use Newton’s method to approximate an intersection point between f(x) = tan(x) and g(x) = 2x. Use…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral SIn(tan x)…

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Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

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Q: In estimating cos(4x)dx using Trapezoidal and Simpson's rule with n - 10, we can estimate the error…

A: a = -1 b = 6 n = 10   h = (b-a)/10 = 0.7 h = 0.7   f(x) = cos(4x)   f'(x) = -4sin(4x) 0 = -4sin(4x)…

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

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Q: Estimate the error if S3 (Simpson's rule with n= 8) was used to calculate sin(2x) dx . a) O lerror|…

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

A: The solution is given below in the next step:

Q: Find the point at which f (x) =2 cos (x) equals its average value on the interval [0, 7] 3 Note:…

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Q: Determine the value of ſo1 3.1 X cosx dx by using N= 4 of the trapezoidal rule. Round-off to three…

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Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: 2. Integrate the expression below using Trapezoidal Rule with interval width of 3.00 units. (sinh x…

A: In the question we have to solve the given integral by Trapezoidal rule with interval width of 3…

Q: 2. Find the linear approximation to hly)=sin(y+1) at y=0. Use the inear approximation to approximate…

A: linear approximation.

Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

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Q: 2- Evaluate sin x dx using i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

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Q: Use the trapezoidal rule with n = 8 to approximate cos(x) -dx Keep at least 2 decimal places…

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Q: 7 1 dx using the midpoint rule with four subdivisions to four decimal places. In(x) Approximate The…

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Q: 2 sin x f(x) = 1+2cosx 5. Pvaluated at x = 1 rad

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Q: Evaluate sin (x) e-x dx by use Simpson's rule. h=0.5

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Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

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Q: 8. Use Simpson's rule, with n = 8, to approximate fe sint dt. Compute the error if the true value

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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: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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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: In estimating : cos(4x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: Compare the Trapezoidal rule and Simpson's rule approximations to x sin x dx and find a bound for…

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Q: 5) Approximate -dx 1 +: Using the Trapezoidal rule and Simpson's rule with h=1. Find an error in…

A: We have to use both numerical methods for 4 subintervals as h=1 and (b-a)=4.

Q: I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. (a). Find the linear approximation to f(x) = sin x at = 0, (b). use it to approximate sin(-0.01).…

A: We have to find the linear approximation and percentage error.

Q: 4. Use Midpoint Rule, Trapezoid Rule, and Simpson's Rule with n =. 4 to estimate f V1+ cos a dx.

A: Given integral :

Q: B.Determine the values of n and h required to cprovimate sin3xdx to within 0.0002. Use Composite…

A: Error in calculating the integral I=∫abf(x) dx by using composite Simpson's rule is given by…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.