i.Show the derivation  of Euler's formula for the solution of ODEs from the 1st principle utilizing Taylor series. ii.Without any derivation, state the fourth order Runge-Kutta formula for solving IDEs.N.b make sure all terms used are defined.

Q: Q3- Find the Complex Fourier series for: * x(t) 디 -7 -6 -4 2 3 8 9 time -2

A: The signal graph is as follows: To find the Complex Fourier Series of this signal.

Q: Find the first four terms of the Taylor series for the function 3 about the point a = 1. (Your…

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Q: Can you help me with the question in this picture? I have to find the Taylor series of the function…

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Q: Let A = 0 2 (a) Compute A², A³, and A4. (b) Find a formula for A" for any integer n ≥ 1?

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Q: Given the periodic function over the period [-π/2, π/2] f(x) = x|x|

A: Sol:- First check given function is even or odd. fx=xxf-x=-x-x=-xx=-fxHence , given function is…

Q: EX: Find the a bout [7=2 taylor series of Pizda 1 2Z+5

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Q: a. Find the first four nonzero terms of the Taylor series for the given function centered at a. 13…

A: We will find the required.

Q: -7<Xく -% -%くxく 0 0<ズく% %くズく fea)= a + 2X N -2ズ fex) = -1<ズくO 0くXく1 b) |3|

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Q: Exer. 81-82: When computations are carried out on a cal- culator, the quadratic formula will not…

A: The first formula is denoted as x=-b±b2-4ac2a and the second formula is denoted as x=2c-b∓b2-4ac. We…

Q: Find the first four terms of the Taylor series for xcos(2x).

A: first four terms of the Taylor series for xcos(2x).

Q: Q5) Find the complex exponential Fourier series representation of the following signal 1 -2 -3 3 -1

A: We will be using standard definition

Q: Let A = 21. (a) Compute A², A³, and A4. 02 (b) Find a formula for A" for any integer n ≥ 1?

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Q: a. f(x) = 7 cos(-x), a = 0

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Q: Find

A: We find Fourier coefficient and put it into Fourier series.

Q: Find the first three terms of the expansion (4 – 2x)°. О а. 4(1 +...) O b. 2°(1 – + O c. 2° (1+ * O…

A: To find the expansion.

Q: Q) for the following function: (X+ 4) - 4 <x<-2 F(x) -X - 2sx< 2 (X – 4) 2 sx< 4 1. Draw the…

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Q: Find the Taylor Series for the function f(x) = ax3 + bx? + cx + d about the point x = 2. What is the…

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Q: oc. Σ 31-1)*(x-1) k=0

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Q: Q3; Find the Fourier series expansion of a Triangle function for (-x5xSx). (25 mark)

A: We will find the fourier series expansion of a triangle function for ( -Pi ≤ x ≤ Pi )

Q: 6 Use substitution to find the Taylor series at x = 0 of the function 1-4x ... What is the general…

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Q: 00 f(x) = x³ at z = 4 as Cn (x – 4)". E Cn (x - 4)". n=0

A: Expand Taylor series of f(x) at x=4 to find value of constants