Use Taylor's residual formula to give an estimate of π / 4 = tan − 1 (1) (without to use the π button on the calculator):  Show that the residual term E1 (1) is in between −1 and 0 and that π / 4 is equal to P1 (1) - 1/4 = 3/4 with an error less than 1/4

Q: Find the smallest positive root by using Newton- Raphson Method \( f(x)=cos(2x)-x^2 \) with two…

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Q: Using fixed point iteration, find the first approximate root of the equation cos x=3x-1 up to 4…

A: Part(1): option(2) is correct Given cosx=3x-1 →cosx+1=3x   So

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Q: [4] (a) Use the most accurate three-point formula to determine each missing entry in the following…

A: Here, h = 0.1 3-point endpoint formula for f'-0.3:…

Q: Q4. Find the Fourier sine series for the function: f(x)= 0 for 0<x< 1/1 for 1/1/1<x<

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Q: Q2: Find the Fourier sine series for the following periodic function. f(x) =x - T<x<7

A: The given function f(x) is odd function, ie. f(-x)=-f(x).

Q: Approximate cos(x) for /x/< T/4 using Taylor Series (polynomial) with a true error of no greater…

A: Please check step 2 for the solution.!

Q: The current I(t) in an LC series circuit is governed by the initial value problem below. Determine…

A: In this question, we solve the initial value problem by using the Laplace transform and properties…

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

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Q: Q2 (a) Sketch the following function of period 27. f(x)= |x| (-1 ≤ x <n) f(x + 2x) = f(x) (b)…

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Q: 4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0<x<T Sketch…

A: If the function is over half 0 to L then it is half range Fourier  series the half range Fourier…

Q: b. Find The Fourier series for the function defined by -n < x < 01 0<x<n S (T + x f(x) = -

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Q: Use Bisection method to find roots of the followings: a. f(x) = e¯*(3.2 sin x – 0.5 cos x) on the…

A: Note: According to our guideline we will answer the first question as the exact one is not…

Q: 一Tく*<0 f(x): (x-1, u+1,

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Q: (1) The coefficients (b, ) of the Fourier series of the function f(x)=|sin x; -7<x<7, is

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Q: The approximation of /= cos(x³ + 5) dx using composite Simpson's rule with n=3 is: 3.25498 0.01259 O…

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Q: Q1: Find the Fourier coefficients and Fourier series of the triangle function f(x) defined by (E+ x,…

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Q: 2020-2021 Choose the Correet answer for the following: 1- da y= sech x is equal to: for a) sech x…

A: As per the guidelines we are supposed to solve first three parts. If you want solution of any other…

Q: Find the graph of the given function over a one-period interval. 1 y = -3 tan 3x Which of the…

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Q: 7.(a) f(x) tan (In x) + 52 7.(b) f(x) = log2 (tan r) + In (¹)

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Q: 3+ cos (8x) Perform a test to determine if x converges. 1/8 2 dx x/8 (Type an exact answer, using n…

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Q: Given that y(t) is an even periodic function with period T, write down an expression for the Fourier…

A: Given  : y(t) is an even function To find : Fourier series expansion as trigonometric functions and…

Q: Q: Find the Fourier series of the function in the defined period: y = |3 – x| ,-4 > x < 4

A: Given function is y=f(x)=|3-x|, -4≤x≤4 The Fourier series of the function f(x) in interval -L≤x≤L is…

Q: 1847 In x 5)- b) Show that the ode (x + tan-¹ y)dx + y dy = 0 is exact, then find the general…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: 1. Find the Fourier Series of the function: S0, -7< x< 0 li, f(x) 0 <x<

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Q: (c) (i) Find a Fourier series representation of the function given by f (x) = x² for -T < x < T,…

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Q: Test the ff ODE for exactness and find the general solution of the DE. (2x + 3y) dx + (3x + 4y) dy –…

A: Let's find.

Q: Use the Newton Raphson Method to find the root of f(x) using 2.2 as the starting value of x. Iterate…

A: Given that the function is fx=arctan(x2+x-6).It is required to use the newton Raphson method to find…

Q: = In(2- sin z) with Given sin z + e -2 0. Using the rearrangement z z0 = 0.5. what is the value of…

A: The fixed point iteration method is a step-by-step method to find the approximate solution of the…

Q: Q2: Employ fixed-point iteration to locate the root of S(x) = sin ( vx)-0.5 x Use an initial guess…

A: Ans: x= 0.525

Q: Given sin r + e - 2 0. Using the rearrangement = In(2 – sin z) with 0.5, what is the value of a5…

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Q: L = {cos (–5t)} L = {e-3t sin (5t) } 5 s2+25 (s+5)+9 s2– 25 (s+3)+25 s2+25 (s+3)–25 s2+5 (s+5)+25

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Q: 4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0<x<n Sketch…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 12. Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: solve one real root of e* – 2x – 5 = 0 with æo = -2 using the Fixed-Point teration Method until…

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Q: Given sin r + e* – 2 = 0. Using Fixed-Point Iteration with the rearrangement %3D T = In(2 – sin a)…

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Q: 5) Give a big-Oh estimate, 0(x³), for the function f(x) = (1+ 2x + 2cos x + 2x2)(log x² + 3|x| + sin…

A: 5 Given that the function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx......1. We have to estimate Ox3 and…

Q: For the given periodic function, S(x) = nx 4 The coefficient a, of the continuous Fourier series…

A: Given: The periodic function f(x) = 0    ,      -π≤ x≤ 0πx4  ,     0 ≤x≤π To determine: The…

Q: - Suppose that for a certain leat-cutter ant colony, the birth rate is modelled by: B(t) = 23,000 –…

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Q: Solve for x(t) for the given ODE with initial values. x"(t) + 0.25x(t) = 0 with x(0)=3 and x'(0)-4

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Q: Calculate the approximate solution of Euler's method in [0,4] for the ODE y' = cos(y) and the…

A: Given equation is  y'=cosy To approximate solution of the given ODE with initial condition y0=0 and…

Q: 5- For each of the following equations, determine an interval [a, b] on which fixed-point iteration…

A: We are entitled to solve one question at a time. As all parts are different, so we are doing first…

Q: B. Find the Fourier series of the periodic function f(x) = sin(x) 0<x<T

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Q: Determine the Fourier series for the periodic function. f(x) = Problem 2 -2, when -π <x<0 +2, when…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q1// Expand f(x) = sin(x + n) , 0<x<; in a half range sine series

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Q: In a dilapidated abandoned building, a cockroach population C(t) (where t is the time in years)…

A: Given that, In a dilapidated abandoned building, a cockroach population C(t) (where t is the time in…

Q: (d) Derive the formula 1 + X 1 In 1 - x tanh-'(x)

A: # We are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 3. The coefficients of the half-range sine expansion of the given function f (x) = 3 sin 2nx, for…

A: To find the coefficients of the half-range sine expansion of the below function for 0&lt;x&lt;1.…

Q: (a) Calculate the first six iterates in the iteration Xn+1 = 1+0.3 sin(x„) with xo = 1. Choose other…

A: The given recurrence relation is: xn+1=1+0.3 sinxnx0=1

Q: Evaluate L{e (cosht – sinh nt)} 3r S+3 A. (s+3)*-n² (s+3)-a² S-3 B. (s -3)- (s-3) 2. s+3 C. (s+3) +*…

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