6. Using the Taylar's theorem, find the approximate value of sin(0.4) with the error value being calculated up to less than 10.

Q: Using Newton's method, the approximation of the root x of f(x) = 2 – x² – co within 10 starting with…

A:

Q: 6. Use the Successive Approximation method to find correct to four significant figures a real root…

A:

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: 2. (a) Find the tangent line approximation to sin(x) near r 0. (b) Is the tangent line approximation…

A:

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

A:

Q: 6. Find the values of 0 in [0,27) where the tangent line of r = 2 + 2 sin e is horizontal or…

A:

Q: A function is given by f (x) = x³ (2.3 sin x – 5 cos x). Compute the root between a = 4 and b = 6…

A: We have to find the root of the following function between a=4 and b=6 using Bisection method,…

Q: Use Newton's method to approximate a root of the equation 3 sin(x) = x as follows. Let x1 1 be the…

A: The given equation is: 3sinx=x Let x1=1  be the initial approximation  To find the second…

Q: Find the slope of the tangent line to the sine function at the origin, (a) y = sin(4x) 15 y'(0) = 4…

A:

Q: (3) Estimate the error involved in using the approximation cos x = 1- for |x| < 0.01

A: To estimate the error involved in using the approximation cosx≈1-x22 for x≤0.01 The Taylor series…

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

A:

Q: The height of an arch above the ground is given by y = 10 sin sin x , for 0 < x < T. What is the…

A:

Q: Use Newton's method to approximate a root of the equation cos (x² + 4) = x³ as follows. 2 be the…

A: Given equation is cosx2+4=x3. To approximate a root of the equation when x1=2.  Formula for Newton's…

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: Given, ∫(1+tan2θ)dθ  The antiderivative of sec2kx is 1ktankx+C The antiderivative of K f(x) is K…

Q: 15. (a) Calculate e with an error of less than 10-6. (b) Estimate the error in the approximation…

A: a. Let fx=ex We know that the Maclaurin series is fx=ex=1+x+x22!+... The remainder term is…

Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, X3- f(x) = 1 – 5x sin(x), xo…

A:

Q: by using Newton Raphson method; find the root of f(x) = sin x – e-x In the interval [0,1] for 4…

A: given f(x)=sinx-e-x       ; 0,1                since root lies in the interval   0,1     we choose…

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: 2. Use the Newtons method to find the root of x-cos.x=0 correct to 3 decimal places starting with x…

A:

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

A:

Q: use a geoetry formula to find the exact value of the definite interval (-2x+4) dx on the interval…

A: The given function is (–2x+4) with the interval [0,3].

Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

A:

Q: Solve for the value(s) of x over the interval 0 < x< 360 sin(2) = - V3

A: values=?

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: ∫(2+tan2θ)dθ Formula ∫sec2θdθ=tan(θ)+C

Q: 2.) Determine the root of the equation by Newton Raphson (should converge at seven decimal places)…

A:

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

A:

Q: 2. Use Newton-Raphson's Method to find a root of the equation correct to 2 decimal places.(ɛ=0.01) x…

A:

Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let x1 = 1 be the…

A:

Q: Use Newton's method to approximate a root of the equation 5 sin(x) = x as follows. Let x1 = 1 be the…

A: Newton's method: Here, f(x) = 5 sin(x) - x and x1  = 1 which is the initial approximation. And…

Q: Find the x-coordinates of the points of inflection of k(@) = sin (e) on the interval 2 Use exact…

A: h(θ) = sin2(θ)  [ -π/2, π ]

Q: 2. Use Newton-Raphson's Method to find a root of the equation correct to 2 decimal places.(ɛ=0.01) x…

A: The given problem is to find the approximate root using Newton raphson method at accuracy upto 2…

Q: 4. Determine one real root of 8 (sin x) e¯* – 1 = 0 with xo = 0.30 using Newton-Raphson Method until…

A: Determine one real root of 8(sinx)e-x-1 =0 with x0=0.30 using Newton-Raphson Method .

Q: 8. Suppose that the tangent line to the graph of ƒ(x) = r0) at r = 1 is equal to the tangent line to…

A:

Q: Use Newton's method to approximate a root of the equation 2 cos (a² + 4) = x° as follows. Let x1 2…

A: Let's find.

Q: Use Newton's method to approximate a root of the equation cos (x² + 4) = 2³ as follows. Let x1 = 2…

A:

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

A: Solution

Q: Find the roots of the equation: sin(x) = x² – 4x to the correct six decimal places using Newton's…

A: Let the given equation is sin(x)=x2-4x

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

A:

Q: For the equation sin⁡x=cos⁡(3x), use the Newton-Raphson method to find an approximate solution. Use…

A: *given:- sinx = cos3x. &amp; x_0 = 0.5.

Q: Find the linear approximation of f(x)=sin(x) at x=2π3 and use it to approximate sin(121∘). Give…

A:

Q: Let F(x) = / sin(5t2) dt

A:

Q: Find the root of the equation f(x)=e*-sin(2.x) starting with x, by Newton Method, with absolute…

A:

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: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

A:

Q: Use Newton's method to approximate a root of the equation 5 sin(x) = x as follows. Let x1 2 be the…

A: The given equation, 5 sin(x)=x

Q: What is the value of the integral S sin(6x) arctan(sin 3x)dx? 2 c) 6 а) 3(т — 2) b) d) 6(т — 2) е) п…

A:

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: 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 .

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.