Consider the initial value problem 0 -1] t [0] j' = | + F(0) – a. Form the complementary solution to the homogeneous equation. jc(t) = c1 + C2

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Q: Evaluate the double integral S, S f(r,0) dA, and sketch the region R. 5. S2 , V9 – r? dr de

A: We have to evaluate the integral ∫0π2∫239-r2 dr dθ and sketch the region R.

Q: 3) ) What are all the fourth roots of i (that is, i'A)? ser and every z with z" 1, we have f(z) =0…

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Q: 2. Among 500 graduating students, 210 of them smoke, 258 drink alcoholic beverages, 216 eat between…

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Q: Prove that any ball (open, closed, half open) in R³ is path connected. or or

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Q: Given the signal x'(t) below. x'(t) (a) Find X(jw) the Fourier transform of x(t). (b) Use properties…

A: We are given the following signal. So, the expression for x'(t) is x'(t)=0,     -∞<t≤-22,…

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Q: Consider the following two matrices: -1 4 2 1 A = 2 -1 B 3 1 3 -1 -2 Which of the following four…

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Q: Find first five terms of the sequence. An Зп + 1 bn = (-1)"n² 2n Сп n ||

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Q: Discount printers manufactures two types of inkjet printers, a consumer version and a business…

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Q: {"p} : Which of the sequences {a,} converge and which diverge: n+(-1)" 1-n? 1. а, 3 2. а, 70 – 4n? n

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Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2rtx) cos(50tt), where x…

A: Solution :-

Q: 1. Prove that any ball (open or closed half open) in R³ is path connected. or

A: Definition: A topological space X is said to be a path connected space if given x, y∈X there exists…

Q: Find the moving trihedral and the curvature at any point of R(t) = (t²,– cos 8t, sin 8t). -

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Q: In each of the following situations, indicate whether f = 0(g), or f = 2(g), or both (in which case…

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Q: 7. Let U = {2, 3, 4, 5, 7, 9}, X = {2, 3, 4, 5}, Y = {3, 5, 7, 9}, Z= {2,4, 7, 9}. a) Draw a Venn…

A: We have given  U = {2, 3, 4, 5, 7, 9}  X = {2, 3, 4, 5}  Y = {3, 5, 7, 9} Z = {2, 4, 7, 9}  Here, U…

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Q: a. Find the percentages of votes cast for Republican and Democratic House candidates in 2010 and…

A: Note: We are entitled to solve only one question at a time and up to 3 sub-parts only. As the…

Q: If f is bounded and integrable on [a, b] sch that 1f(x) | 0).

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 1 Σ 3n2 + 6…

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Q: Let T(x): be the Taylor polynomial of degree k of the function f(x) = sin(æ) at a = 0. Suppose you…

A: Using alternating series approximation

Q: Show the following series is conditionally convergent. (-1)*

A: To show that the given series conditionally convergent.

Q: Define linear Volterra integral equations a solution of the Volterra integral equatio:

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Q: Use Newton's method to approximate a root of the equation 4x° + 4x +1 = 0 as follows. Let x1 = - 1…

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Q: Write each of the following permutations in two-line notation. 1. (1 2 3)(4 3 2)(1 2 5) E S5 4 5 5 2…

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Q: Use long division to determine the decimal expansion of . You can either: 12 90 1) Show your work on…

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Q: Find the radius of convergence, R, of the series. (-1)" 7" 00 Vn n = 1 R = Find the interval, I, of…

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Q: price of a jumper was reduced in a sale by . The new price was later reduced by . What fraction was…

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Q: prove that 3^n is greater than n^3 for all n greater than or equal to 4

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Q: Consider the two series: 2n + 3 (a) 2 n2 In n n=1 8. 1+ (n – 2)! (b) n! n=1

A: Given series are: ∑n=1∞ 2n+3n2lnn∑n=1∞ 1+n−2!n!

Q: QUESTION 23 For the directed graph shown below, determine the reachabi ity matrix. O. O a[110 1 1 10…

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Q: Consider the system of differential equations -7y2, +7y1. a. Rewrite this system as a matrix…

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Q: Of the following operations, which one is the fastest? a. - b. > C. + d. X

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Q: Approximate the root of the following function using bisection method, approximate error <0.00001 1.…

A: We know that the bisection method is used to approximate the root of the function by repeatedly…

Q: For a certain type of ight the number of hous a bub will bum beforerequing replacement tenamean of…

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Q: Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 convergent or divergent. b)…

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Q: Calculate 373,755,967,102 x 389,291,774,965 mod 100.

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Q: Find the solution of: y'' - y = 56e^(3t) With y(0) = 9 and y'(0) = 6. y =

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Q: Does the sequence { an} converge or diverge? Find the limit if the sequence is convergent 5n? an…

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Q: 2L (1-сos(nn)) ппх f(x) sin dx = (пп)з (1-сos(nп)) Σ 4 f(x) = -(1 -cos(пп)) sin (пл)3 L n=1 8

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Q: Again, the function y=x is shown below. Graph each of the following more complicated quadratics…

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Q: Problem 3: Show that the partition P= (7, 6, 5, 4, 3, 2, 1) is not graphic. Solution:

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Q: Give the demain and range of the relation. 4) {(1,8), (-1, -8), (-7, -4), (6, 0)}

A: The given relation is  R= {(1,8),(-1,-8),(-7,-4),(6,0)}