Example 6.15. Using modified Euler's method compute (1.8) where y is governed by the following IVP with h = 0.2. dy = 2 + 1 √ty 1, y(1) = 1; dt

Q: m} be positive integers s orollary 4.3. Let f(x) € Z[x] and {m₁, irwise co-prime and m = m₁m₂ mk.…

A: There are two questions and student didnt mention any particular question to solve so i am solving…

Q: Show that the following relation is not a function on R {(x, y) ∈ R × R : x = cos(y)}

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Q: 3.13. Consider the function f defined on x = [-л, π]: (27, | 3, x1 x=1' f(x) = Find the Fourier…

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Q: Problem 4 Suppose the function f has n + 1 derivatives at the point xo, and let = xo + 0x (x − xo)…

A: As per the question we are given a function f(x) which has (n+1) derivatives at the point x0 And ξ =…

Q: 2t x = t(e²t + 4) y=x −x+e*(x+cosx)

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Q: By showing that any sequence in A ∪ L has the same limit as some sequence in A, prove that A ⊆ A ∪…

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Q: Prove that 2¹ >1+n√2¹-1 ; \n > 2 where n is a positive integer.

A: Since you have posted a multiple questions we will solve first question for you as per our Q&A…

Q: dy 4. -+x-y dt 2r+212

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Q: Find the particular solution: d³y d²y +2 = dx3 dx² 0 when x = 0, y = -3, y' = 0, y = 12

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Q: imitregang nom-Mangott let na libe be my and 1(n) be function, we have EX (d) = logn din

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Q: Example 6.24. Using Milne's method, solve the differential dy (t+y) dt 2 equation for y(2), given…

A: dydt=t+y2 t 0 0.5 1.0 1.5 yt 2 2.636 3.959 4.968 Note: We are allowed to solve one question…

Q: x=t(e²¹

A: We have x=te2t+4

Q: (b) The front body vibration vertical displacement, d of a moving train after departed from a…

A: Given  Time,t(s) Vibration vertical displacement,d(m) 1 0.03 1.3 -0.16 1.4 0.1 2.23 0.23…

Q: 6.) [D³ + 6D² + 11D +6] (y₂) = 0 7.) [4D³ + 4D² +D] (ro) = 0 8.) [D¹ + 2D³ + 10D²] (y₂) = 0

A: (6)…

Q: Let B: I + e₁2e3 + е3 e₁ where I is the identity tensor in R³ with basis vectors (e₁,e2, e3). What…

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Q: a. Set up an integral for the area of the surface generated byrevolving the given curve about the…

A: The given curve is x+y=3 from (4,1) to (1,4). We have to: (a) SETUP an integral for the surface area…

Q: Use the modified decomposition method to solve the following Fredholm integral equa- tions: 3. 6. 8.…

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Q: Example 6.24. Using Milne's method, solve the differential dy (t + y) dt 2 equation. for y(2), given…

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Q: use the noise terms phenomenon to solve the following Fredholm integral equations !- = x (1 + √5/2²…

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Q: Let a and b be positive real numbers. If a, A₁, A₂, b are in arithmetic progression, a, G₁, G₂, b…

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Q: Recall that Pn is the vector space of polynomials p(x) of degree at most n with real coefficients.…

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Q: Consider a vector ? in a linear vector space of dimension ? spanned by basis {?̂?}. You need to…

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Q: 6. [²3 Find the eigenvalues and eigenvectors of A =

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Q: 1. y=x²e + 4e* 2. y e-3x cos3x

A: As per our guidelines we do here only first question and kindly rest question can be reposted.

Q: determine whether the sequence is monotonic,whether it is bounded, and whether it converges. an =…

A: Given the sequence an=2n-13n. To determine whether the given sequence is monotonic, whether it is…

Q: what is a mathematical model? What are the two basic components of a mathematical model?

A: Answer given below.

Q: Consider the group GL₂(R). Let A (a) Find all elements of H = (A). (b) What is A|? √2 2 √2 2 NANS √2

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Q: Let D be the set of letters in the English alphabet with the usual order. Define ⟨D² , ≤⟩ such that…

A: Given D is a set of letters in English alphabet and the order in the set is considered as the usual…

Q: Find the answer and simplify. If possible, write the answer in its rectangular form. log(3 − 3√3i)

A: Given, log3-33i   We have to find the answer and simplify.

Q: Give an equation for a transformed sine function with an amplitude of 3, a period of , and a phase…

A: Given That : Amplitude  =3 Period =π4  phase shift =π5 To Find : Transform equation of sine function…

Q: 6. Use the following form graph of yos-2 is the below 162 que lo miog snil letnosion of 20 (anato…

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Q: v=x²e=x + 4e²

A: Given solutiony=x2e-x+4ex

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A: Given That : The function fx=x2/3y1/3 where x is the number of labor hours and y is the number of…

Q: What is the importance and application of random number? Give at least 3 real life applications.

A: We will discuss the importance and application of RANDOM NUMBER. Then we will introduce 3 real-life…

Q: (a) Prove that 1 1 ¹ + ( ₁ + }) ( ) + ( ¹ + 2 + 3 / ) ( 21 ) +1+ 52, 5 5² 2² (c) Find the sum of…

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Q: What's wrong? Consider the rotation field F (-y, x) x² + y? * a. Verify that the two-dimensional…

A: The given vector field is, F=-y,xx2+y2. (a) To Show: Two-dimensional curl of F is 0 and double…

Q: 1, solve the following Fredholm integral equations by using the Ado- mian decomposition method r1 1.…

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Q: Proof: 1. Prove that for any x integer (x + 5) is odd (3x + 2) is even

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Q: d³y dx3 Find the particular solution: d²y +2 = dx² 0 when x = 0, y = -3, y' = 0, y" = 12

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Q: 2. In every Pythagorean triangle, prove that at least one of the sides is divisible by 5.

A: The given problem is to prove that in the Pythagorean triangle there is atleast one of the sides is…

Q: Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer…

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Q: Find the sum to infinity of the series 1 − 3x + 5x² − 7x³ + .... ∞

A: (a)

Q: 1- Which one of the following is equivalent to 3 mod7 a. 73 b. 31

A: Answer given below.

Q: the sum of

A: Part (a)

Q: A variable plane pes through a fixed point (a, b, c) and meets the uses at A, B and C. Show that the…

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Q: Gompute у сом) у (005) вд y by corrector method where differential eqantron zet-z dy/dt = and y and…

A: dydt=2et-y t 0 0.1 0.2 0.3 y 2 2.01 2.04 2.09

Q: Show that cos λx 2² +1 -dλ TU že 2 x ≥ 0.

A: Given: x≥0 To show:∫0∞cosxλλ2+1dλ=π2e-x.

Q: Let H be the set of all points (x, y) in ℝ2 such that x2 + xy + 3y2 = 3. Show that H is a closed…

A: Given That : Suppose H is the set of all points x , y in R2 such that x2+xy +3y2=3. To Show : H is a…

Q: Find the answer and simplify. If possible, write the answer in its rectangular form. Re((−i)−i)

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