Using the power series method about x = 0, the recurrence relation of the differential equation: y" + xy + (x² + 2)y=0 is:

Q: 9.W.1 The Gram matrix of an inner product on R² with respect to the standard basis is G = -1 12 Find…

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Q: 2 Q) Let A € M₁ C4) such that A² = A ENA show that det (I+A) = 2

A: If minimal polynomial is totally factorizable that is product of linear factors. Then matrix is…

Q: The sum of the series n-n+1 n! is

A: Solution : To find, ∑n=0∞n2-n+1n! Taylor expansion of ex around 0 ex=∑n=0∞xnn! put x=1; e=∑n=0∞1n!

Q: Which of the following intervals can be an interval of existence of the solution of the linear…

A: x-12y'-11y = x-113 x-12y' = x-113+11y

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

A: Here we are given a 3d surface S by the following equation : 4x2 - (y-3)2 + 4z2 = 4 And we have to…

Q: Suppose a,b,n are integers and n>0 s.t. 63a^5b^4=3575n^3, what is the smallest possible n. Explain…

A: Solution : -

Q: Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green. (a)…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: describe xy - trace, xz - trace, yz - trace. draw each trace a) z^2 - 4x^2 = 9 - 4y^2 b) z^2 -…

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Q: 2. Show that if the orthogonal dimension of a Hilbert space H is finite, it equals the dimension of…

A: Given: Finite dimension To find: Former finite

Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…

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Q: Which is Larger? 2015/2015! OR 2016/2016!

A: We need to identify , which of the following number is larger. 2015 !2015    or  2016 !2016 This can…

Q: Let f(x) = (3-3x) 5 f(x) has one critical value at A = For x A, f(x) is Select an answer ✓ Select…

A: Solution:-

Q: Consider the equation du - 2y = 0, y(0) = a. Let I = (-1, 1). Which statement below is NOT true? (A)…

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

A: Given  Weight density =9000N/m3 By Pythagoras theorem, CD2+AD2=AC2⇒CD2+1 =22⇒CD2=3⇒CD=3

Q: Find the area bounded by the curve y=-x³x² + 3x and the line y=x. 16 A 8 square units B 16 square…

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Q: Given the periodic function defined in one period by the function: (bt, f(t) = a, (0, 0 0.

A: The following formulae are used to find the Fourier coefficients of the function fx on the interval…

Q: 0,−1), (2,1,0), (3,1,-1), (1,1,1)} spans. {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly R³. y, z) €…

A: Let us consider the set S=1,0,-1,(2,1,0),(3,1,-1),(1,1,1) To check R3=span S that is to check,…

Q: The minimum possible order of a homo- geneous linear ordinary differential equa- tion with real…

A: The minimum possible order of a homogeneous linear ordinary differential equation with real constant…

Q: 1. Verify that y = e²x + 3xe²x is a solution of the ODE y" - 4y + 4y = 0. (Show all work when…

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Q: 2. Given the figure below, find a single vector that is equivalent to C B tw b) 10 14 וד --(A-F+C) G…

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Q: Which of the following function has the Macularin series (-1)"4"x² [(-1)"4" 1 n=0 A. 1 B. 1 - 2²

A: Given the Macularian series                                 ∑n=0∞-1n4nx2n

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

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Q: III. Let and be vectors such that 7=(2,2,-1), ||||= √√2, 7-=-3, and x = (2,1,2). 1. If u = (-2m,…

A: When two vectors are parallel, one vector is represented as a non-zero scalar multiple of the other…

Q: The graph y = f(x) is transformed to y = -f(x + 3) - 2. Which describes the effect of the…

A: Transformation of graph is very significant in studying the analytical nature of a function. The…

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: f¹[V√2x In (√x)]³dx CS…

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Q: Prove that span (v1,v2,...,vn) is a valid subspace of R

A: Let V = R is a vector space. Let S = v1 , v2 , ..... , vn We need to show that   span(S)  is…

Q: Find the transition matrix from B to B'. B = {(0, -1, -2), (0, 4, 1), (1, 3, -3)}, B' = {(1, 0, 0),…

A: We find transition matrix B to B'.

Q: Let n ≥ 1, x be a real number, and x ≥ −1. Prove the following statement using mathematical…

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: 2- Every finite set in any topological space is:

A: every finite set is any topological space is COMPACT

Q: Find the maximum of the following function F(x) = 1 - 8x + 2x² - 4x³ + x² + x³ - £xº A)…

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Q: By using the method of least squares, find the best line through the points: (2,-3), (-2,0), (1,-1).…

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Q: In an engineering lab, a cap was cut from a solid ball of radius 2 meters by a plane 1 meter from…

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Q: 2. Given the figure below, find a single vector that is equivalent to D B a) E-A tw IA tu F to G

A: given vector bundle

Q: the volume of the solid in the first octant bounded by using z = 1+x² + y² and z = 4 using…

A: The volume is the amount of space occupied by the closed surface. It is measured in terms of the…

Q: aluating the moment of a planar lamina, a horizontal strip cannot be used as a representative area.…

A: Given,         A. In evaluating the moment of a planar lamina, a horizontal strip cannot be used as…

Q: verse of a Matrix I. Use the determinant test for no singularity to determine hether items 1-5 of…

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Q: Determine the Laplace Transform of sin³3t

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Q: The sum of a positive factor of pq is p+q+pq-1 None of them p+q+pq p+q+1

A: The factors of pq are 1, p, q, pq. So, the sum of the factors is 1+p+q+pq i.e. p+q+pq+1 Therefore…

Q: Consider f(x-m+ A) 14/3 B) 5 C) 6 D) 17/6 ·S= 3x5 3x4+6x33x2 - 6x B C + x-1 x+1 x+m A x-m+ + -dx.…

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Q: Diketahui polinominal f(x) = 2x²-5x²+2x+1 dan g(x) = x²+ax-2 jika f(x) dan g(x) bernilai sama, untuk…

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Q: find the distance from A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

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Q: Let f C D be a function, with C being the domain and D being the codomain. Show that for any C₁, C₂…

A: Solution: Let  x ∈ fc1∩c2⇒∃  y∈ c1∩c2such that fy=x⇒y∈ c1 and y∈ c2⇒fy ∈ fc1 and fy ∈ fc2⇒fy ∈ fc1∩…

Q: Use secant method to find the root of x^3 –x^2 – 3x – 3 with two initial points xa=3 and xb=2 and ∈=…

A: Ffind the root of equation using secant method

Q: - Q4: A- Choose the correct answer for the following: 1- A cofinite topological space (X, T) is: a-…

A: As per our guidelines we are supposed to answer only first question.  I have  solve only (1) in very…

Q: (d) Find a basis for the column space of A. CHIE

A: Solution : Given, A=12100251103722-210237-18 d) To find basis for the column space of A:…

Q: 2. Solve the ODE using Separation of Variables. dy dx 5x²+4 y+1

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Q: O (-2)² (-3)4 123 +123 O 418 O216 x 215 O 317 x 417 O 1217 +1217 Submit

A: An expression is a factor 1217 if it is a multiple of 1217. Lets check each answers individually

Q: 2. What is the largest possible c in (1) if X=R² and x₁=(1,0), x₂ = (0, 1)? If X = R³ and x₁ = (1,…

A: Given: c To find: a) X=R2b) X=R3