Let I:= [a, b] and let f: I -> R be a continuous wetion such that f(x) >0 for each x iN I. Prove that here exists a Number of >0 such that f(x) > α for all XEI.

Q: Let f(x) = 3 + cos (5 a) where 0 < x < 2π. Next we do a Fourier series expansion of f(x). The…

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Q: when values of theta are small approximations are sometimes used for trig functions sin theta, cos…

A: 1. Sine Function (sin(θ)):Approximation: Small angle approximation  for small angles in…

Q: Follow the steps below to solve the given differential equation using series methods. Assuming the…

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Q: Consider the following differential equations. x = 4y², x(7) = 1 P(y) = dx Find the coefficient…

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Q: 4. (i) Show that 2 is a primitive root mod 11² = 121. Hint: Use the criterion given by Lemma 6.4 and…

A: Basic facts on primitive roots will be used.

Q: Show all calculations. Show that the following competition model does not admit closed orbits when…

A: We have a competition model represented by a system of differential equations.The goal is to…

Q: Thank you so much, could you perhaps elaborate the proofs a bit more, I understand it but somehow it…

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Q: Use the limit comparison test to determine whether an = (a) Choose a series an lim n→∞ bn = lim n-x…

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Q: 2 3. (a) Consider the function f(x) = x - x + 1 and starting point x₁ = 0. Show that the sequence…

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Q: If you let G and H be two groups and consider the product group G x H and let K be the subset of G x…

A: The objective of this question is to prove that the quotient group (G x H) / K is isomorphic to H…

Q: 'I' F. ds for the given vector field F and the oriented surface S. In other words, find the flux of…

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Q: Find a particular solution ₂ to by trying a solution of the form [a] -1 cos(4t). -15 0 5 cos(4t

A: (.) given matrix is,       (.) If  is a particular solution then it's satisfies the system of…

Q: The function T: R² R³ ->> 3 0 T(v) = Av = 2 Determine T(v), where v = (2, -1) Show that I' is a…

A: The given function is defined as .(a) we need to find  for .(b) We need to show that  is a linear…

Q: 2. Solve the simultaneous congruences x = 4 (mod 5) and 2x = 3 (mod 7)

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Q: f(t)=t, g(t) = 1

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Q: Sketch the graph of the function below and determine its Laplace transform. u(t-6) -u(t-8) Click…

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Q: 8. Write down the integrals for finding the volume of the solid generated by revolving the region…

A: Given, region bounded by the curve y=ex , the lines y=e and the Y−axis .

Q: 1. (1) Show by hand¹ that 2 is a primitive root mod 19. (ii) Find² a complete set of primitive roots…

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Q: Evaluate the following integral So axebx² Where a = 0.3 and b = 0.56 Give your answer to 1 decimal…

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Q: (a) 1·1! +2·2! + . . . + n •n! = (n + 1)! − 1 - (b) if n > 6, then 3″ <n!

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Q: оо 2п п 1 = |A² f f fe 2r dr dp sin de 0 0

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Q: Given the state-space equations X(t) = [21]x(t) + [1] u(t) y(t) = [1 0]X(t) +u(t) (u(t)= 1,t≥ 0) If…

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Q: Solve y + 2y + 10y -90( 15), y(0) = 1, y (0)

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Q: Given the graph on the right, which statement is FALSE? a) The degree equals the number of direction…

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Q: 7. 8. What is the horizontal asymptote of f(x) a) y = 2/1/20 b) y = = 3x+47 2x-1 c) y = 121/12 What…

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Q: Graph the following conic section, identify the vertices, foci, directrices, and asymptotes (if they…

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Q: Use the convolution theorem to obtain a formull y"+y=g(t): y(0)-0. y(0)-3

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Q: 2) Use Cauchy Integral Formula to evaluate integral z³ - 9e² z-2 where C is the counter |z| = 3 fo C…

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Q: 1. Consider a function f(x) = x² + x² 3 2 4x - 4. (a) Compute the minimum number of iterations…

A: Given Information:The function is given as .Objective:c) Find the exact roots of the function…

Q: IfA=[] is an nxn matrix, then the trace Tr A of A is defined to be Tr A-a₁a22. The characteristic…

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Q: Find f(t). f(t) = 3s ~{28=13} s²(s + 1)³

A: We have to find .

Q: . Express dw dt as a function of t using chain rule where sin (x+y)+sin (x+z) + sin (y+z), dw and x…

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Q: Use Table 12-1 to calculate the future value (in $) of the ordinary annuity. (Round your answer to…

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Q: 2. Let V₁ a. 14 -2' b. V₂ = " 16 10 spanned by B. Note that B is an orthogonal set. -49- 35 7 -28_…

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Q: Consider two groups, G 1 ​ and  G 2 ​ . Group G 1 ​ is defined as {1,a,a^2 ,a^3 } with operation ⋅ ⋅…

A: this basically states the following that any 2 cyclic groups of the same order are isomorphic.

Q: For each of the following functions f, determine if it is injective (one-to-one), surjective (onto),…

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Q: lowing values. ㅏ t) = 2t e 20et 35et x(0) = + 18- -t e [] eAt 3 4e2t-e-t 4e2t - 4e-t - e

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Q: Find f(t). f(t) = L 6s - 1 s²(s + 1)³) {

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Q: Prove or disprove that [x/2] = [(x+1)/2] for all real numbers x . Prove or disprove that [x/2] =…

A: We disprove by giving a counter example

Q: a¹³ Uij = 0 in 2. Set Problem 3. Let u be a smooth solution of Lu = v = |Vu|² + \u². Show that Lv ≥…

A: To show that Lv≥0 in Ω for sufficiently large λ, let's compute…

Q: Following question is from a linear algebra course, We consider a second basis of V, C = {1 + X, X +…

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Q: P.) Consider the topology r = {GCR: 0 € G or G=0} on R. Is [0, 1) compact in (R, 7)? Explain why.

A: Given, topology  on defined by, Consider the open cover of  in (Since,  is open set in  for every…

Q: 1) Suppose T is a linear transformation of TH=2-3x + x² and T[3] =1-x² T[2¹] and T Determine. R² to…

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Q: 4. Consider the following identity: 2 Σ(3) - (30) (2n). (1) Perhaps it seems mysterious? But if you…

A: We use basic counting techniques to solve this problem.

Q: 1 A с B 2 4 3 F D E G 5 7 6 H 8

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Q: Let A = -11 107 9 -2 and b 5 3 7 = = Define the linear transformation T: R² R³ by T(T) = A. Find a…

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Q: 1. is this given problem belowe com be considered as lineau programmning? If not, convert or Find an…

A: The objective of the question is to determine whether the given problem can be considered as a…

Q: The matrix A = [-62 -12] 285 55 A₂ = -5 with eigenvector v2 A EDE¹ where E-¹ is E and D is the…

A: The matrix  has eigenvalue  with eigenvector  amd eigenvalue  with eigenvector .Forming the matrix ,…

Q: (10) t=3 mo A t=4 mo B t=1 mo (30) (20) (40) D F t=3 mo C E t-3 mo t=3 mo (50

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Q: Please help with finding these solutions Find the general solutions of the system. x(t) = 6-90 = 1…

A: According to Bartleby guidelines I have solved first one