Consider a positive integer 1 < i < 9. Then, given T(n) = 2T([n / 2] + i) + n, show that T(n) E O(n · Ig n).

Q: 1. Try to use the ratio test or the root test to determine if the following converge or diverge. If…

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Q: 4.) Find the value(s) of k such that A is singular. 1 k 2 A = -2 -k 3 1 -4

A: The given matrix is                               A=  1  k    2-2  0 -k   3  1 -4 We have to find…

Q: Show that g(t) takes on the value 0.499 for some t in [0, 1]. t +1

A: Given that g(t)=0.499 we need to find t

Q: Find the value(s) of k such that A is singular.

A: The given matrix will be singular if the determinant of it is 0

Q: TQ residue of f(z) = e (z – 1) (z + 9) at z = -9 is 10e-9 :Select one True False

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Q: dn-1 for all n E Z with n > 2. Prove that for a 2. Let d = 2, and d, neN, d, =. %3D %3D %3D

A: Mathematical Induction is a special way of proving things. It has only 3 steps: Step 1: Show it is…

Q: (-1)" Σ Given: sin = x²n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let xn ≥ 0 for all n ∈ N. (a) If (xn) → 0, show that (√xn) → 0. (b) If (xn) → x, show that (√xn)…

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Q: 0 <m < n such that am = e. (Hin

A: Subgroup generated by any element in a finite group will have at most n element where n is order of…

Q: 3.18 Suppose if x = 0, f(x) = if z e (. where n e N. Prove: f € R[0, 1], even though f has…

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Q: Consider the following IVP: x" - 4x' + 4x = 4e2i; x(0) = -1, x'(0) = -4 Find the general solution. A…

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Q: Prove if equal to MPn (W) dx= 2" (n!)" (2n+)! that m is an integer

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Q: 4. Work either (a) or (b), NOT BOTH (a) Let In = for n E N. Prove that nIn = 0. 0, n n%=D1

A: a. Given that    In=0,1n  for  n∈ℕ. And we have to prove that…

Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

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Q: Answer the following questions by a proof or dis-proof. What is the big-O estimate for f(n) = 87 log…

A: To find- What is the big-O estimate for fn = 87log543n + 2n3log37n2 + 4n3n + 7 ?

Q: (c) Two real numbers X and Y are chosen at random in the interval (0, 1). Compute the probability…

A: Let's assume that set of numbers X,Y|X,Y∈0,1 form a unit square, whose vertices are (0, 0), (0, 1),…

Q: 2. Use the Root Test to determine absolutely or diverge. 4n+3\ n (a)E-1( Zn=1 Зп-5) (b) E (-In (e²…

A: As we have to use the root test , So first I have written the Root test then using them for both the…

Q: Let c be a  positive integer, then (e^c+1)≥e^c for all c.T/F

A: Given that c is positive integer and we have to check whether the given inequality is true or not.…

Q: (a) Find the least positive k E N such that 3* =10 1. (b) Using this k, prove: for all m e N, 3m =10…

A: (a) find the least positive k∈ℕ such that 3k≡10 1 b) using this k prove that : for all m∈ℕ 3m≡103m÷k…

Q: Is there some time t, 0 < t < 8, such that R'(t) = 0? Justify your answer.

A: Given: The below table is given, To find: Any value of t in the interval 0&lt;t&lt;8 at which…

Q: 3, Re call Eudlid's proof of In finitude * primes! Shouw that T Cx): = 1{ ps X: p-pinae }12 logz…

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Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: O we N. P.M. to estimate the root of -X for on initial guess of Xo

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Q: Given that n21 and xn = V5n2 + 2n -3n 00 1. Will {xn}, be divergent or convergent? 2. Will E=1Xn be…

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Q: H.W Given a sequence x(n) for 0sns3, where x(0) = 1, x(1) = 1, x(2) = -1, and x(3) 0, compute its…

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Q: Suppose that 0< fn < In on X for all n e N. If gn 30 on X, then fn 30 on X.

A: Solution:-

Q: 84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

A: Answer (a): To prove : ex≥1+x if x≥0 The given inequality can also be written as: ex≥1+xex-1-x≥0

Q: (30) Prove the following inequalities: log x 1 (a) Vr € R \{1}, X - 1 - √x (b) Vn € N, e- e − ( 1 +…

A: Given,a) log xx-1&lt;1x , ∀x∈R*+\ 1b) e-1+1nn≤ e2n+1 , ∀n∈NWe will use Mathematical Induction…

Q: For any n large enough, prove E" ) – = 0(1). k=0

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Q: Let Z N(0, 1) and let y = [Z], where, for a real number x, [x] denotes the largest integer not…

A: Given,  Z ~ N(0,1) PDF of Z is given by, fZ(z) = 12πe-z22 ; z∈R Given, Y = Z So, Y = Z = 0if…

Q: Show that g(t) = t2tant takes on the value ½ for some t in [ 0 , π/4 ].

A: gt=t2tant on the interval 0, π4. When t=0, g0=02tan0=0 When t=π4, gπ4=π42tanπ4=π2161=π216=0.6168

Q: For f(x) = x³ - x +4, compute the formula for n+1 in Newton's method. - In +4 - 3h - In 3a급-1 | In +…

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Q: Σ (-1)n+1 n3 n=1 11. Find an upper bound for the error in the above approximation |S – Sg].

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Q: at k ( k) = n(k-₁) fo 1) for in

A: To prove, knk=nn-1k-1

Q: 2. (a) For n ≥ 0 and x E R, prove that (b) Prove n n Σ ^ (^.) 2^* (1 - 2)"-* k k=0 = = In. n x)n-k…

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Q: Let X be a xỉo. Calculate a+o², so that P(X <a)=0.25. Provide a numerical answer only, no need for…

A: We have given that  χ210 Find a+σ2 P(x&lt;a)=0.25

Q: Differentiate f(N) = (N) = 0 bN² + N with respect to N. Assume that b and K are positive constants.…

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Q: n2 for all n E N. 4n Let r, :=

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Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: Find the sum of (arctan(n + 1) – arctan(n)) if exists. Lütfen birini seçin: a. b. 3 2 d. e.0 DOO

A: Given- ∑n=1∞arctann+1-arctann To Find- The sum of the above expression.

Q: Formally prove the T(n) = (5n – 4)° is O(n³). Show all work and all steps to receive full credit.

A: Order: T(n)=(5n-4)3 T(n)=(5n)3-3.(5n)2.4+3.(5n).(4)2-(4)3T(n)=125n3-300n2+240n-64

Q: Find the value(s) of k such that A is singular.

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Q: The characteristic of Zs[x]/ is 6. 3 O None of the choices

A: The characteristics of the function

Q: for a>0 is defined a n(x² + a²) and sin ax = (x)"6 prove that la * fb = fa+b and ga * 8b =gmin (a,b)

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Q: Let c, = M and Cn = 2cn-1 - 1 for Vn eZ+ - {1}, find the explicit formula for the nth term for n…

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Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: d'y It is given that y=(1+x)² In (1 + x). Find dx 3 Prove by mathematical induction that, for every…

A: First it is required to find

Q: Prove that e“ p.w. on R. n! n=0 M8

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Q: 3 (a) Given that T= 2n12g , express I in terms of T, g and n. %3D

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