The refractive index n of a piece of glass is related to the critical angle θ by n = 1/sin θ. Assume that the critical angle is measured to be 0.70 ± 0.02 rad. Estimate the refractive index, and find the uncertainty in the estimate.

Q: Show that the average value of sin^2t over [0,2pi] is equal to 1/2. Without further calculation…

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Q: Find the length of the curve using formula.  y= ln (cosx) bounded by 0 and pi/4

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

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Find the value of u in the interval 30°, 90°4 in decimal degrees, if sin u = 0.27843196. Give the…

A: sin u=0.27843196⇒ u=sin-1(0.27843196) Now by using a calculator, we have…

Q: Find the length of the curve over the given interval. r = 1 + sin θ, [0, 2π]

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Q: Find the length of the following curve: y = ln(cos(x)) from x=0 to x=pi/4

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Q: at f" si sin rdr = 2, find the average value of the sine function on the interval [0.7]. Also, find…

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Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

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Q: Apply the composite Trapezoidal, composite Simpson's and composite Midpoint rules to approximate…

A: Use the following formulae, to obtain the solution. Composite Trapezoidal Rule:…

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

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Q: After choosing the appropriate trigonometric substitution the integral -dx, becomes

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Q: The coefficient of sin ( 2x) in the antiderivative of

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Q: Sin x3D%=

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Q: Find the average power of the signal: x(t) = cos x + sin x %3D

A: Given: To find the average power of the signal: x(t)= cos x + sin x

Q: sin

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Q: In the given question , find the arc length of the graph of the function over the indicated…

A: Given: y=lnsinx,    for x∈π4, 3π4.

Q: sin ede 1- cos e 8.

A: The integral of sinθ is given by -cosθ and the integral of cosθ is given by sinθ. The basic formula…

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: 4) Given y = 3 sin 2x, Find the Amplitude Interval and Period (x/2, 0) (0, 0) Amplitude interval…

A: Hshshs

Q: By using Beta function, the integral I tan(0) d0 is

A: To find value of integral∫0π2tanθ3dθ by using Beta function. Bm,n=ΓmΓnΓm+n…

Q: Given x sin x + 1 = 0, using Newton-Raphson method with initial guess X0 = 4, calculate the root of…

A: Given that, the function is x sinx+1=0 and the initial guess x0=4. Note that, the formula for…

Q: Without graphing the function y = 5 sin(3x), determine its amplitude, period, and the distance…

A: Given equation is y=5sin3x   .....1

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫√x sin2 (x3/2 - 1) dx, u = x3/2 -…

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Q: . Estimate the root of the expression, f (x) = x² – cos x, using: d. MOSS using xo = -1 with error…

A: As per the question we have to find the root of the equation : f(x) = x2 - cos(x) = 0 With tolerance…

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: Find the arc length of the graph of the function f(x) = ln(cos(x)) ㅠ π [153, 5 Use the tables to…

A: Arc length of y=f(x) on a, b is  L=∫ab1+f'x2dx We have f(x)=lncosx given interval π9,π5

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: 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 points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: Given that S." sin xdx = 2, find the average value of the sine function on the interval [0, π].…

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Q: Find the arc length of the graph of the function over the interval. y = In(sin z);

A: Given,          y=lnsinx ; π4,3π4

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: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: I am going to solve the given problem by finding the arc length of the given parametric curve to get…

Q: Use Newton's Method to find an approximation to V25 correct to within 10-6 (use an appropriate…

A: Solution

Q: To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

A: The exact value of the given integral is 1

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 distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find…

A: Please see the explanation below

Q: 6. Using the Taylar's theorem, find the approximate value of sin(0.4) with the error value being…

A: We are entitled to solve only one question at a time  To find - The approximate value of  sin0.4 by…

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

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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: Find the linear approximation to sin(x) at the point x-0 and use your answer to approximate the…

A: Given f(x)= sin(x), a=0 we know linear approximation, L(x)= f(a)+f'(a)(x-a)

Q: Consider 3x+ sin x − ex= 0, using Secant Method with initial points X0 = 0 and X1 = 1, calculate the…

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Q: Given that ſ♫ sin xdx = 2, find the average value of the sine function on the interval [0, π]. Also,…

A: Please see the below picture for detailed solution .

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.