21-30. Estimations with linear approximation Use linear approxi- mations to estimate the following quantities. Choose a value of a that produces a small error. 21. 1/203 22. tan 3° 23. V146 24. V65 25. In (1.05) 26. V5/29 27. e0.06 28. 1/VI19 29. 1/V510 30. cos 31°

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Q: Use Newton's (or the Newton-Raphson) method and find p3 with po = 0 for f(x) = cos(Tx) – x. O -80 4.…

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Q: Find the maximum and minimum values for the position of the boat. The position of a boat at time t…

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Q: Eliminate the parameter t from the following. x = sin t − 5, y = cos t − 4

A: Eliminate the parameter and simplify it.

Q: Using Newton's Method to solve -4z - cos(z) =0. with an initial approximation of zo =6, the value of…

A: Here given -4x - cos(x) = 0So Letf(x) = -4x - cos(x)thenf'(x) = -4 + sin(x) x0 = 6

Q: 3. Using both Simpson 1/3 and 3/8 rules compare the Error of the equation. -dy 1+cosy

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Q: A weight on a spring is bobbing up and down. Its height above the ground at time t is h(t) = 5 + cos…

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Q: 4- Using the data sin(0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin…

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Q: Repeat Exercise 6 using the Secant method. Reference: exercise 6 Use Newton's method to find…

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Q: An RCL circuit connected in series with a resistance of 4 ohms, a capacitor of 1/26 farad, and an…

A: This question is about application differential equation.

Q: Find the solution of the equation 4rsina +2 cos 2a - a = 2 using the Newton-Raphson method with an…

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Q: 2. i) Find in radians the values of x in the interval 0°0 and 2 is and acute angle. Hence find the…

A: The problems with the trigonometric functions for value of x can be solved using the trigonometric…

Q: 1. Use Newton's method to approximate a solution of 4V = 1+x² in the interval [2, 3] to five decimal…

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Q: A mass of 1 slug is attached to a spring whose constant is 5 Ib/ft. Initially, the mass is released…

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Q: 4. Let f(x) x² + cos(Tr). f&)= Qx -Tsin(Tx) (a) Use Newton's method to find the root of f(x) with x1…

A: a) Given f(x)=x2+cosπx  with x1=-12=-0.5    f'(x)=2x-πsinπx  we know Newton's formula to find…

Q: 2. Cosinder the following initial value problem (IVP): = 1+z sin(ry), 0<I<1, (0) = a +8. (a) Does…

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Q: Find the solution of the equation 4xsinx +2 cos 2x a2 2 using the Newton-Raphson method with an…

A: Given:

Q: Find the solution of the equation In(2x- 1) cos(x – 1) = 1.7 using %3D Newton-Raphson method with an…

A: Let f(x) = ln(2x-1)+cos(xπ4-1)-1.7 So f'(x) = 22x-1-sin(π4x-1)π4

Q: 1. An oscillating current in an electric circuit is described by i(1) = 9e¯' cos(2rt) where t is in…

A: Consider the given function. it=9e-tcos2πt

Q: Exercise 3

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Q: Solve 2x + cos a = 5 using Newton-Raphson method and an initial value of with an error less than 5%.…

A: Newton Raphson Method:- For a function f(x) xi+1=xi - fxif'xi; i=0, 1, 2,....   Given equation is…

Q: Find the solution of the equation 4xsinx +2 cos 2x x = 2 using the Newton-Raphson method with an…

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Q: An RCL circuit connected in series with a resistance of 4 ohms, a capacitor of 1/26 farad, and an…

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Q: In  the given equation as follows , use Taylor’s Theorem to obtain an upper bound for the error of…

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Q: 8. ) Which of the following(s) is/are possible to solve the given problem y" - y' +2y = tan(x²)…

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Q: Find the solution of the equation In(2x – 1) + cos(x - 1) = 1.7 using Newton-Raphson method with an…

A: We need to find the solution of the function ln(2x-1)+cos(π4⋅x-1)=1.7 then for Newton-Rapson Method…

Q: 1/9 Determine the trapezoidal approximation of 7 sin 9x dx using 4 equal subdivisions of the…

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Q: Which of the following(s) is/are possible to solve the given problem y" - y' +2y tan(x²) y'(-2) = 0,…

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Q: (4) Let the position of a swinging pendulum in simple harmonic motion be given by s(t) = a cost +…

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Q: NEED ASAP PLSSSS Find the roots of the function g(x) = In(2x-1)+cos(pi/4 x -1) = 1.7 using…

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Q: An RL circuit has an emf given (in volts) by 3 sin 2t, a resistance of 10 ohms, an inductance of 0.5…

A: Given,             dIdt+20I=6sin2t                        ...(1)and  emf=3sin2t…

Q: 2. a) Determine the values of n and h required to approximate e2x sin 3x dx to with in 10-4 by the…

A: Simpson's rule error bound    Es≤kb-a5180n4 , where f4(x)≤k where ∣E​S​​∣  this e absolute values of…

Q: Use a linear approximation to estimate sin 29° Answer: The approximate value of sin 29° is V3 O sin…

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Q: 7. (a) Use Newton's method ONCE with an initial guess of ro = 0.1 to find an approxi- mation to the…

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Q: After one iteration of Newton Raphson Method, what is the refined estimate of the root of 7 (sin z)…

A: We can solve this using newton raphson method

Q: 8:14 PM Mon Feb 28 - 53% T O + : b = 2UT6 生))+()-号) =(-$)(-)+(學)量 b=4 65 25 - 3 (85) COS S = and cos…

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Q: Find the solution of the equation In(2x – 1) + cos(x – 1) = 1.7 using Newton-Raphson method with an…

A: It is given that ln2x-1+cosπ4x-1-1.7=0. Let fx=ln2x-1+cosπ4x-1-1.7. We have to find the solution of…

Q: 2 Solve the following equations by using Newton-Raphson Method and taking the given point as the…

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Q: 1) Solve for y" + (cos x)y = 0, given that cos x can be represented 1 2! + + 4! as a series of .…

A: Solution : Given, y"+cos(x)y=0 Let the expanded form of y as, y=∑n=0∞Cnxn By differentiating…

Q: - Using Lagrange interpolation formula, find the value of sin points 6 X: 0 π/4 π/2 sinx: 0 0.707107…

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Q: (a) Find the approximations T10, M10, and S10 for 28 sin(x) dx. (Round your answers to six decimal…

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Q: (a) Using the intermediate value theorem, explain why there is a solution of this equa- tion with…

A: From the Basic Calculus

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

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Q: Consider the initial value problem: v(t) = cos(t)+ y(t) – 5, v(2) = -1. Use the improved Euler's…

A: Please check step 2 for the solution.!

Q: 1.Use Newton's method with the specified initial approximation x1 to find x3, the third…

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

Q: 11) A particle moves along a line so that at time t its position is s(t) = -4 sin 5t, where s(t) is…

A: We will use second derivative test to find time at which maximum veolcity achieved

Q: ³ (³) x sin(x) = cos Using the following method, determine the smallest positive value of x that…

A: From the graph, it's clear that the smallest positive root is near to the point x=1.Hence we can…

Q: 2. By using Simpson's rule with N = 4,8, and 16 Integrate the following functions SOLVE PART B eX…

A: We need to use Simpson's rule to evaluate the integral. So, we need to find ∫0π4Tan X dX If we need…