. Derive the Adams-Bashforth Three step method by the following method. Set Yti+1 = Yt, + ah f(t;, Yt,) + bhf(t;-1, Yt,–1) + chf(t;-2, Yt;-2) (3) y expanding yt41; f(t;-2, Yt;-2) and f(t;-1, Yt;-1) in Taylor series about (t;, Yt;) and equate he coefficients of h, h² and h³ to obtain a, b and c.

Q: The linearization at a=0 to √2+5x is A+Bx. Compute A and B

A:

Q: 3. Let d= = [( ) ( ) ( ) ( )], B = [1, 2, 2²), v = (¹). " (a) If f(x)=x²-3x+2, compute [ƒ(x)]ß. -1 2…

A: Our objective is given below:

Q: Question 4 Consider a consumer who consumes three goods, 1, x2 and r3. The consumer's consumption of…

A: Given: x1(p, s, w, y)=p2yw-sy=0             x2(p, s, w, y)=3yw-1sw=2             x3(p, s, w,…

Q: Consider T(r1,12, Ia) = (371 – 212 + 4ra, I1 + 273, 12). Find T!. %3D

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Q: Suppose f(x, y) = xy + 4. Compute the following values: f(x + 4y, x – 4y)= - f(xy, 6x²y³)=

A: We can find the given function .

Q: 1.4 Which of the following equations are linear? (iii) x = -7y + 3z (i) x + 5xy – 2z = 1 1 (v) VTx +…

A:

Q: Let B = {1, t − 3, (t − 3)² } and C = - - {1, t − 2, (t − 2)²} - be two bases for P2. The function…

A: a=1b=-2c=5Explanation:

Q: 9. Given the functions /(x) = 2x + 5 and g(x) = x? – 4, find (4) x. b. C. d. 2x-5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let f(x,y) = 2* + 7xy, find f(0, – 3), f(- 3,2), and f(3,2). f(0, – 3) = (Simplify your answer.) f(-…

A:

Q: (a) Find the domain of V4 – 3w R(w) = w + 2

A: Please complete your question b part its incomplete. What is l ? Here I'm doing (a) part only.

Q: The values of a and b, for which the function f(z) = x³ + axy² + i3x?y + iby³ is analytic, where z =…

A: Given function is f(z) = x3 + axy2 + i3x2y + iby3 by comparing f(z) = u +i v here u = x3 + axy2  and…

Q: Find a linear approximation y = f(x) = x5 − 4x² + 4x³ − 12x² + 21x − 6 to the following function at…

A:

Q: 3. Consider the functions, m(x) = x + 3x and p(x) = 2x + 5, Find m(p(1)) b. Find m(p(x)) a. c. Find…

A:

Q: r(0)=, find v(t) and r(t).

A:

Q: Let B = {1, t − 3, (t − 3)² } and C = - - {1, t − 2, (t − 2)²} - be two bases for P2. The function…

A: a=1, b=-2, c=5Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Find f(k-1) when f(x) = 5x² + 3x + 6. OA. f(k-1)= -7K² +5k+8 OB. f(k-1)=5k2-7K+8 OC. f(k-1)=5k²-7k+…

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Q: Given f(x, y) 90x + 80y - 2 – 4y? – xy, and evaluate f(8, 5). f(8, 5) = %3D

A: Given : fx , y = 90x + 80y - 2x2 - 4y2 - xy  To fine : f8 , 5 Solution : For value of fx , y , put x…

Q: Suppose product i (i  1, 2) costs $ci per unit. If xi(i 1, 2) units of products 1 and 2 are…

A: As per the question, we aim to determine the optimal quantities of two products, given their…

Q: If f(x,y) = In(x?y² +3x) find- дудх O a. 12x?y (x²y² + 3x)? O b. 6x?y (x2у2 + 3x) Ob. 6x²y (x²y² +…

A:

Q: a55 dx20y3 if f(x,y)=x. ez A- Find B- find fxy and fyy if f(x.y)= y+x²y+4y³- In(y2+1) C- Find the…

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Q: r = |7| , ř = 2xi – 3yj + zk let V(2r), v°(r) find all of

A: Vector Differentiation

Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

A:

Q: Compute fx, fy and fz for the function and evaluate them at the indicated points

A:

Q: 1-t2 -i+ t+2 j+ In(t + 2)k. Find the domain of r(t) t2+1

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Q: Findthe line thatcontains the error, explai the error, and thenconvert the problem correctly. f (x)=…

A:

Q: Prove that at the point of intersection of the surfaces - (-) where y = x tan 0 the die of curvature…

A:

Q: Q14- If f(x,y) = 2xy - x² Iny- 2y² + 3x + 4, then axy is : for the function

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.