Which of the following refers to backward - difference formula? Why? You can give your own example to answer the question why. a.) f'(x) = y ≈ Y₁+1, b.) f'(x₁) = y₁ ~ Yi-Yi-1, C₁) f'(x₁) = y₁ ≈ Yı+1-yl-1 2h X1+1=Xi *Ị-XI-1

Q: Question 4 4.1. Find a power series representation for the function 8 using summation 2x-15 sign,…

A: Power series expansion rational function:  interval of converges :

Q: Solve the linear system using both gauss-jacobi and gauss-seidel x₁ + 3x₂ - x₂ = 5 3x1 - X2 = 3 x₂ +…

A: Apply the following steps, to solve the given system of equations by the iterative method.…

Q: Put I, in equ (1) 80 = 61 + 6( 1² + 1) 12 3 -- I = 7amp.

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Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. - a. What type of quadric is S?…

A: Since you posted multiple questions, we will solve first part for you. Kindly repost other questions…

Q: 18. Figure F is graphed. Transform figure F using the rule (x,y) → (x-8,-y). YA 10 8

A: Introduction: Graph transformation is the process of modifying an existing graph or graphed equation…

Q: By changing to cylindrical coordinate, evaluate So So -1 c√1-x² 16 x² + y² x² dzdydx

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Q: For all sets A, B, and C. Is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement. You may justify…

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Q: Show that the three functions: f₁(x) = ex-8f2(x)= ex, f(x) = 4(2x-2) are linearly dependent.

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Q: using the following: a = 2i + 3j + 6k, b = i - j - k a) find the component vector of a onto b b)…

A: Given a = 2i+3j+6kb = i-j-k

Q: Evaluate the volume under the surface given by z = f(x, y) = x² + y, over the region bounded by the…

A: Imagine a parallelepiped with small base area dA with height z, then volume of this parallelepiped…

Q: 1. Trapezoid JKLM with vertices J(-6, 6). K(-3,7), L(-1.3), and M-8, 0): (x, y) (x+7, y-3) J'() K'…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find a power series representation for the function 8 using summation 2x-15 sign, determine the…

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Q: be a linear operator on a vector space V(F). If = 0, t ce oft and null space of t. Also given an…

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Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

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Q: 17. Find a combinatorial proof that n("z ¹) = (k+1)(²1). k 19

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Q: c). For each of the given paths, verify Green's Theorem by showing that [y³dx + xºdy=ff(xXx dA.…

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Q: (2) If c(z) ≥ 0 for all z = [0, 1], then a function minimizes J(v), that is, J(u) = inf J(v), with…

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Q: Question 2: Show that path connectedness is topological property. Explain and show your work.

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Q: ule? How to solve by both methods? Ju he final answer

A: solution find using trapezoidal and simpson 3\8 rule

Q: 1-x 2+3 Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line l : = y + 1 = 3 2…

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Q: Solve the differential equation using inspection method d'y d³y dx5 dx³ = 24.

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Q: Find the orthogonal matrix and upper triangular matrix in matrix A using QR method

A: The given matrix is                           A=20-40-204-26

Q: Exercises To Solve [No.5] Lim 5 9-5 dx -x²8x-15 D "Cosx dx Sin x+25inx+5 b

A: 5)  Let , I = lima→5 ∫a-4 dx-x2 - 8x - 15 Let , us simplify denominator first ,  -x2 - 8x - 15 = -x2…

Q: The graphing calculator window shows the graph of a function f(x) and its derivative function f'(x).…

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Q: ion of the trace of S on the xy-plane, yz entify each trace. he traces obtained in (a). Label all…

A: Given as, 4x2 - (y-3)2 + 4z2 = 4

Q: Determine the solution to the given ODE: y = √1-y² over the interval from x=0 to 0.5 using a step…

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Q: Solve the following differential equations: 1 √1-3x (a) - dx + sin y dy = 0 cos 2y +1 (b) x²y + x³…

A: Using separation of variables for first problem and using integrating factor for second problem.

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

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Q: 6. Find a basis for the null space of the functional f defined on R³ by ƒ(x) = §1 +§2 − §3, where x…

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Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Introduction: The definite integration of a real valued function over an interval is the area that…

Q: 10. Let z₁ and z₂ denote complex numbers. Show that (Z₁, Z₂) = Z₁ Z₂ defines an inner product, which…

A: Z1 and Z2 are orthogonal iff <Z1, Z2> = 0

Q: c. The quadric S can also be identified as a surface of revolution. Find a generating curve for S on…

A: Given,  S: 4x2-(y-3)2+4z2=4 is a surface of revolution Since the coefficient of x2 and z2 are same,…

Q: Evaluate [√x² + y² ds_ along the curve r(t)=(4cost)i+(4sint) j+3tk, −2π ≤t≤ 2a.

A: To find- Evaluate ∫Cx2 + y2 ds along the curve rt = 4costi + 4sintj + 3tk, -2π ≤ t ≤ 2π.

Q: Rectangle A is the pre-image, and rectangle B is the image. Find the scale factor for this dilation.…

A: Given: Rectangle A is pre-image and rectangle B is image. To find: Find the scale factor for the…

Q: 7. xdy = (5y + x + 1)dx

A: xdy=(5y+x+1)dx ⇒ dydx=5xy+1+1x⇒ dydx-5xy=1+1x

Q: Let A be a nxn square matrix having rank 2 then rank of (A^t A) is (A^t= Transpose of A)

A: Let A be a n×n square matrix and Rank (A) = 2

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: We will use integral to find force on trough . 1st will find force on a horizontal slice of trough…

Q: 2. y" - y = x, y(0) = 1, y'(0) = −2, h = 0.1 from x = 0 to 1.

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Q: 8. If Z is an (n−1)-dimensional subspace of an n-dimensional vector space X, show that Z is the null…

A: Given: n-1 dimensional subspace To find: Scalar multiple

Q: 4. If (x) is a sequence in an inner product space X such that the series converges, show that (sn)…

A: It is given that xj is a sequence in an inner product space X such that the series x1+x2+⋯…

Q: IV. Consider the plane : +3y - 2z = 6 and the line with parametric equations l:x=4-3t, y=2+t, z = 2t…

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Q: Sketch f(t) and find the Laplace Transformation of the following functions

A: The function in which its output repeats after regular intervals of the input is called the period…

Q: 2. Determine the zeros and poles of the recursive equation below. y[n] = x[n − 1] − 2x[n - 2] + 2x[n…

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Q: Find the differential equation which has the given family of integral curves. The family of circles…

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Q: 0 -2-4 8 15 1. A = 1 4 1 6

A: We need to find the determinant of the given matrix using raw operations and cofactor method…

Q: Given the polar curves: C₁:r = 2 cos 0 π 2 C2 B(0,0) C₁ A(2,0) C₂:r = 2 cos 30 Find the (sum of)…

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Q: Let A = (0,1]-{\n € N}. (a) Find the set Aº of its interior points. (b) Find the set A' of its limit…

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Q: 4. Which of the following subsets of R³ constitute a subspace of R³? [Here, x = (₁, §2, §3).] (a)…

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Q: 6. Show that the closure Ỹ of a subspace Y of a normed space X is again a vector subspace.

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Q: Q1. Find the multiplicative inverse of 29 modulo 1137. Write down all steps of your computa- tion.…

A: For any two arbitrary integers a and n, if the existence of another integer b is established so that…