f(t) = {b 0

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with -0.1, find the relative error…

A: We can solve this using runge kutta method and relative error

Q: dx Find the value of the integral 14² by using simpson method (n = 6)? 를

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Q: Find the inverse of the given matrix using Adjoint Matrix: 1 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2

A: We know A-λI = 0 A-λI =    1-1   0   0-1   2-1   0  0-1   2-1  0  0-1   2-λ1000010000100001 = 0

Q: B. Find the area of the region bounded by the following: 18. common to 7 = 3 cos and r=1+ cos

A: 18. The given curves are r=3cosθ and r=1+cosθ. To find: The area under the curves . Please post the…

Q: Consider xy' = y(lnx - Iny) with y(1) = 4. Using Runge-Kutta method with h=0.1, the k₁ in the…

A: The given O.D.E is xy'=ylnx-lny with y1=4. To find: the value of A.

Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = 0

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Q: let FC k be a Galois extension with Gal

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Q: the chord joining points the A(x) and B(B) on the hyperbola -= 1 is a focal chord, then prove at…

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Q: For the equation 3y" + y' = 0, find the recursive relation equation. (n — 1) an–1 3n an-1 3n (n — 1)…

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Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, the k₂ needed in the…

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Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' = eV¹- guaranteed by…

A: Please see the attachment

Q: prove, for all integers x, if x mod 3 does not equal 0, then 3 | (x2 +2)

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Q: From a point P on a rectangular hyper hyperbola at A and B. Show that the a constant, independent of…

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Q: Solve the partial differential equation: a²u =²; by the method of separation of variables for a…

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Q: Angela currently owes $6,000 to a friend who is charging her interest of 2.80% p.m. She is required…

A: We have to calculate the size of the equal payments using three months as the focal date. Simple…

Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

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Q: 2. Let R be the region below enclosed by the curves z = 2 − y², y = − sin (772), and x = -1, as…

A: Both cases required to divide the region into two subregions.

Q: Question 3.1. Let's think of the set of n-by-n matrices as R² by using the matrix entries as…

A: Please see the attachment

Q: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of…

A: Given: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis.

Q: - 2x²) y" + 6xy' + 2y = 0

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Q: Suppose the slope of the tangent line at any point on a curve is x+4yz. If the curve passes thru…

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Q: the first four terms to ximate the sum of the series:

A: Given,                ∑n=1∞1n2+1

Q: How may chords are there in the figure? [1] (134°-50°1/2-42" 4AFC-134* 4EFD-50*

A: chords are the line segment whose  both end points lie on the circle.

Q: When approximating f(x) dx using Romberg integration, R4,4 gives an approximation of order:

A:

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: 1 f(t) 1 t

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Q: 8 Σ η = 1 (x-4)*-1 3η η

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Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: du J²u D = 0, x>0, t>0 Ət əx² u(x,0)=0, x>0; u(x, t) →0, xx, t20; u(0,t) = uo. t20 = We consider the…

A: Solution : For difference equation to be invariant, ∂u∂t-D∂2u∂x2=0 u~=aγux~=axt~=aβt…

Q: Assume that the nth term in the sequence of partial sums for the series no an is given below.…

A: Sequence of partial sum for the series         ∑n=∞an  is   Sn=5+8n22-7n2 (.)   Behaviour of a…

Q: Let C be the curve connecting (0,0,0) to (1,4,1) to (3,6,2) to (2,2,1) to (0,0,0) Evaluate Lex (xx +…

A: We will use Stoke's theorem to solve the following problem

Q: 2 2- X dy dx dy d x y +34 X/2 e Sinx x 2

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, y(1.3) = y(A)…

A: Solution:-

Q: Determine if the series converges or (5-2n)" diverges: Σ 6n n=1 n Converges by the P-Series Test O…

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Q: Set p(t) = COS t 0≤t≤2 To otherwise For -∞ 0 for x = (0,4) (iii) Thus (f* g) * h = 0 whereas f * (g…

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Q: 5. Consider the equation x₁ + x₂ + x3 = 18, where 2₁, 22, and 23 are integers. How many solutions…

A: This question from number theory.

Q: 5. Given the function f(x) = 1 + ex sin(4x) with integration limits from a = 0 to b = 1. Use…

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Q: Let f: RR be a function satisfying f(x + y) = f(x) + f(y) for all x, ye R. If the function f(x) is…

A: Note :   Let r>0 and c∈R ,then vr(c)={x∈R : x-c<r }=(c-r ,c+r) ,which is called r…

Q: Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method with h=0.1, the k3 in the…

A: The given differential equation is: y'=y(lnx-lny)x., y(1)=4. and h=0.1. Given: k3 is in the form…

Q: 5.1.12. (-) Prove or disprove: Every k-chromatic graph G has a proper k-coloring in which some color…

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Q: Are the Following Vectors Linearly Dependent or Independent? (3,-2,0,4),(5,0,0,1),(-6,1,0,1),…

A: Vectors v1, v2, v3,..........vn are linearly independent if for scalars c1, c2, c3,.........,cn such…

Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

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Q: When using Euclid's algorithm to find the GCD of 820 and 730, what are the first three remainders…

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Q: is the condition such that the straight lines joining the origin to the other two points of…

A: Given: Curves equation   ax2+2hxy+by2+2gx=0a'x2+2h'xy+b'y2+2g'x=0

Q: Determine the value/s of D if the graph of the equation x² + 4y² + Dx - 4y + 2 = 0 a single point;

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Q: 12. Show that the set of all constant polynomials in Z[r] is a subring but not an ideal of Z[x]

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Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: Suppose the slope of the tangent line at any point on a curve is curve passes thru (1,3),…

A: We will find approximate value of y at required point  and then find  slope of tangent line . Using…