QUESTION 1 Find the half range sine series for f(t) and use this to state b, when n = 11, for f(t) = t2 - 3, 0

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

Q: e a) Consider the function f (x) : (х — 1, —п <х<0 . Is this function even or odd? lr + 1, 0<x < T…

A: Given

Q: Question 6. The temperature u(x, t) of a narrow metal rod of length L by the heat equation: = 1 is…

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Q: QUESTION 3 What is the value of the sine series, at x=1, for the function x if 0<x< 1 8 (x) = 5x if…

A: The given problem is to find the value of function at x=1 , we have to check the function for given…

Q: Question 9 Find n so that T, (trapeziod rule with n subintervals) is guaranteed to approximate |…

A: ∫05cos(2x) dx       to within 0.01We have to calculate for the n

Q: Question 4 If cos(1) is approximated with the help of the series cos(x)= 1- + 2! 4! Then the…

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Q: QUESTION 6 A bottle of juice with a temperature of 95 F was taken off a shelf and placed in a…

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Q: QUESTION 3 x"+x'+3tx³ = 2et x(0) = 3 x'(0) = 4 %3D %3D At = 0.2 %3D Use the Euler method with a time…

A: Euler's Method: Euler's method is used to approximate the solution of differential equation of the…

Q: QUESTION 12 At the end of the 3rd iteration of the secant method, how many significant figures of…

A: Please check step 2 for solution.

Q: QUESTION 2: Test for exactness, and solve the Initial Value Problem for the following first-order…

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Q: QUESTION 4 x' = 12 t2 x, x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately…

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Q: Question 1. Let f(r) = sin r. Subdivide the interval [-27,0] into four subintervals of equal width,…

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Q: Question: 10 Consider the function f(x) = mcos.x – sin x. Find the constant m if = 4

A: Given  f(x) = mcosx - sinx  Find the value of m if f'(π/2) =4

Q: QUESTION 3 Use Newton's method as shown in class to find the root between 0.0 and 1.0 AND for a root…

A: Newton Raphson method

Q: Question 5 The sine Fourier series of the function 1- cos (zr)+ cos (2zr)- cos (3zz) for the period…

A: Age here if we put -x in function  then it will come same function  it means it is the even function…

Q: 5) Use the first three terms of the Taylor expansion for f(x) sin(x) to estimate sin(-1/4).

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Q: Question 12 Evaluate: f 0 tan (0)d0 O E arctan 0 + arctan(0) 0 +C 21 O arctan(0) 0 2 arctan 0 + C 21…

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Q: Question 5 a) Solve tan(x) = 5 in the Interval 0sxS 360°, giving your solutions to 2 decimal places…

A: The solution of an equation of x in a given interval is the values of x in the interval which given…

Q: S0, -7<x < 0 f(x) = {1. 0 Sx< 2. Find the sine series of [x, f(x) = 0 < x < #/2 T - x, 7/2 <x<

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Q: TS Problem 3: f (x) = 2 - x2, 0<x < 2; sine series, period 4 culty t's hear

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Q: Question 4 Find the derivative 4f (x)]; ƒ (x) = log, (sinh(arcsec 4-1) coth (arcsec ( 4-1)) 422-2…

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Q: Previous Problem List Next Determine the sum of the following series. 6. sin sin n + -1

A: Sum=

Q: Question # 4 Represent the following function by a Fourier sine series f(t) = >1 > 0 <t<n 2 EIN

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Q: Question 8 A Which of the following series diverge? sin 2 I. I. 00 () II. +1 A) II only B) I and Il…

A: I have used different test for convergence test

Q: Question 3. Let S(t) - 4+ 3t,0 <t<3 and let the half-range sine series representation of its odd…

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Q: QUESTION 5 The Lower Riemann Sum utilises which function value on each subinterval? a. The square…

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Q: QUESTION 4 x"+2x'+5x = -20 6(t - 2) Initial Conditions: x(C= -6, x'(0) %3D 6 = the Dirac Delta…

A: Given x''+2x'+5x=-20δt-2Initial conditions x0=-6, x'0=4

Q: The series 2 cos(n t) n = 0

A: By integral test we can solve the following problem

Q: Question 7 A The sum of the series 1 +2 + + +.. is ... A) In 2 B cos 2 D) sin 2 E) nonexistent

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Q: QUESTION 5 Solve the following two parts. (a) Write the Fourier series for cos? (x), x€l- n,m) even…

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Q: Question#3: Find the series solution of the following ODE: (l-r²) dx dr dt dx = 21 -(2² + A)x. dr

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Q: IN QUESTION 18, FIND THE EXACT VALUE OF s IN THE GIVEN INTERVAL THAT HAS THE GIVEN CIRCULAR FUNCTION…

A: topic - inverse trigonometric functions

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: I== (0),” 0=(0)," I-= (0)" 0="pt8tstan

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Q: QUESTION 1 x" + 4x'+20x - 20 6(t – 1) %3D Initial Conditions x(0) = 10, x'(0) = -2 %3D 6 =the Dirac…

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Q: QUESTION 7 (i) -2+ (iv) 2.31 The constant a is such that ["xe*dx = 6. (1i) Show that a satisfies the…

A: The find the constant a such that ∫0axe12xdx=6. First find integral ∫xe12x dx. Use integration by…

Q: A certain sine function has an amplitude of 3, a period of n, a phase shift of n/2, and a vertical…

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Q: Problem 1. Let H, denote the n-th harmonic number. Prove that H, + H-1++ H2 + H1 = O(n log n).

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Q: 1. “Middle C" has a frequency of 262 s-¹ [called a Hertz or Hz]. What is the period for this note?

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Q: Question Question 5 of 14 Apply Newton's Method to f(x) and initial guess xo to calculate x1, x2,…

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Q: Question 7: Use the trapezoidal rule with 6 intervals to evaluate * 10 x7 dx ,giving the answer…

A: to find:- Solution of integral function by numerical method as well as by exact method.

Q: QUESTION 1 Given that = 0.2836 approximates f(x) = cos x at x = 5. 1. Find the absolute error 2.…

A: Solution: True value of f(x) = cos x at x = 5 (radian) is         f(5) = cos(5) = 0.2836621855. So…

Q: Question 6. The temperature u(x, t) of a narrow metal rod of length L = π is modelled by the heat…

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Q: Question 6 "If the frequency of an oscillation is 1Hz, it means" 100 oscillation per second 10…

A: The number of oscillations completed in one second is called frequency.

Q: Consider the function f(t) = 12 cos(40t), where the coefficient of t is in rad/s, and tis in…

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Q: QUESTION 4 dx where x# 0 x² In(Ixl) +c In (13x1) +c 3ln (Ix1) +c QUESTION 5 7894 142 Ma

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Q: (a) Find its initial position. (b) Find its positon after 5 seconds.

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Q: Question 2 Write a Riemann sum corresponding to the following definite sin x xp- 1+ x5

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Q: Problem 3. Expand the function f(x) = x, 0< x < 2, in half range sine series. (Hint: Take the odd…

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Q: Question Let x34x 1 0. Determine the root to which Newton's Method converges for the initial choice…

A: We know,