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: If the first five terms of the Taylor expansion for f(x) about x = 0 are 2-3x + === x² + 7 then…

A: we are given the Taylor series expansion for a function f(x) and we need to identify f'''(0)

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A: answer is in next step. please give a like!!

Q: 2. (a) If z = 1+ 3i and v = −2 − i then 1 A. + 2 B. Tin Tin + C. A. 2√6 e-in/6 B. 2√3 e-in/3 D. 2 10…

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Q: Question 5: Which of the following distributions does not have a symmetric form? (a) Z-N(0,1) (c)…

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Q: Find all the values of t so that 8et > 0. O-∞ 21/1/2 8 Otzo

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Q: Consider Newton's Method for calculating √a. (a) Show that the Newton's Method formula is given by…

A: Consider the Newton's method for calculating We have to show that the Newton's formula is given by

Q: Find a basis of solutions of the following equation by the Frobenius method. Try to identify the…

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Q: 2 A = 1 -4 -2 and notice that A? = 0. Compute the matrix exponential e'A using the Taylor series.…

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Q: 3) State the exact error associatd with Taylor polynomiad of degre frx)=X+9 estimating fa)-1 우or…

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Q: ami 3 Find explicit formula for ao = 1, a₁ = 2, an = an-₁ + 2 an-2, cima characteristic polynomial…

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Q: find the first 4 terms of the taylor exapnsion about x 0 Ax) = 2 , Use that to approximate 2

A: From the given problem: fx=2x2.   From the Taylor series:   fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+……

Q: (d) 1 (32-1)(2+1)*

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Q: 9. The two complex numbers V and W represent two reactances connected in series. Calculate the total…

A: Two complex numbers are To Find: Total reactance.

Q: The surface S is given by r(u, v) = 2 cosui +2sinu j+v k, 0≤u≤, 0≤ v≤1. Find the implicit equation…

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Q: When n is large, n! can be approximated by means ofthe expression√2πnnen called Stirling’s formula,…

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Q: Question 3. Given the formula 1. w(a) - use the Taylor series w(+ A) - u(a) + ha(o) +"(0)++ nt 21 to…

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Q: B6. (a) Sketch the graphs of the left and right hand sides of the equation x* = 3 – x. Hence show…

A: B6.  Consider the equation x4=3-x.

Q: What are the first three terms in the Taylor expansion for cos(x) Provide your answer below: a = π

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