T(n) = 2 * T(n/2) + c, for n > 1 T(1) = a

Q: 49. f(x) = alst %3D n=0 Selet ai 50. f(x) = 2 (-1)+1(x – 5)n n5" n=1 * (- 1)n+1(x – 1)"+1

A: f'(x)=∑n=1∞ (-1)n+1n(x-5)n-1n5n      =∑n=1∞ (-1)n+1(x-5)n-15n Apply the ratio test to check the…

Q: f(x) * a = 49 (2n – 1)! 2". 72n + 1 + (x – 49)" n = 1 1 ㅇ윽+>m.72n+ 1.n! 1 (x - 49)" n = 0 1 1:3.5.…

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Q: A production manager determines that t months after production on a new product begins, units…

A: A production manager determines that t months after production on a new product begins,  units…

Q: 3. How many solutions are there to the equation x = e*? Will the iteration Xn+1 = converge for…

A:

Q: 2 (ii) using Convolution theorem. (s+2)(s²+9)

A:

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = A x + x+ x²+ x3 + ... -) +В х x²+ x³ + + x+…

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Q: Find 2x dx. x2-4 (if it converges)

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Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

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Q: The number of computers N (t) (in millions) infected by a computer virus can be approximated by 2.4…

A:

Q: Given f(x) = x²+ 2x - 8 . Using the fixed point iteration method x=g(x), where g(x) is a negative…

A:

Q: How does h(n) = n2 / 2n behave for large whole-number values of n? Does h(n) tend to infinity?

A: Consider the function:      hn=n22n Determine end behavior for the large whole number value of n.

Q: b) Show that MsE(S²) = (п-1)* c) You are given another estimator of o? which is T² = = (X; – X)² i=1…

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Q: Find all values of x for which ) (3x)" converges. n=D1

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Q: 2) Suppose that d₁= .02t 0≤t≤2 0034² 2<t≤5 Suppose that a deposit of X is made at f= 0, and a…

A: We have to find required deposit amount.

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: 51. For which values of a does eax dx converge?

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Q: 2. Solve f e** using Simpson's 1/3 Rule with n = 8.

A: The Simpson's 13rule is given below by,  ∫abfxdx=h3fx0+4∑i=1, i is oddn-1fxi+2∑i=2, i is…

Q: A tumor may be regarded as a population of multiplying cells. It is found empirically that the…

A:

Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: 12 (a) Approximate dtwith a left hand sum and At = 2. t+2 12 (b) Approximate A t dt with a right…

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Q: Find the value of the summation. E (2 – 3) = k= 0 of

A: We can find the summation value as below.

Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

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Q: {in(n² +1) Im(x +4)} 19. А. В. 1 С. 1/2 D. 2 E. Divergent

A: we have to identify the given sequence is convergent or divergent

Q: (i) Find the constant term in the expansion of x+-

A: You have given 3 different questions in picture, without mentioning any particular questions. We can…

Q: For N= 100 and payoff functions P(n) = 10n +9 and S(n) = 8n - 4, derive the formula for the total…

A: Given P(n)=10n+9S(n)=8n−4N=100

Q: 1. Expand x³y²(x + y)12. E15.(15) xn+3y15-n ,15-п а. n 12 b. Eo () xn+3y14–n ELo (5) xn+3y14-n С.…

A: From the given information. The given expression is .

Q: at k ( k) = n(k-₁) fo 1) for in

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

Q: 25. What is the t- critical value? A. 2.131847 B. 2.776445 C. 1.859548038 D. 2.306004 26. What is…

A: Given the the measurements of the heat-producing capacity of random samples of five specimens each…

Q: | #(In(x))" 1 dx converges and Let p be a positive number. Determine the values of p for which the…

A:

Q: 25. What is the t- critical value? B. 2.776445 A. 2.131847 C. 1.859548038 D. 2.306004 26. What is…

A: Here we have to test that average heat producing capacity of two Mines are equal or not. This is two…

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

A:

Q: Describe the long run behavior of f(n) = 3n – 4n³ – 5n° + 5 As n → - 0, f(n) → ? As n → o, f(n) → ?

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Q: -> (6) 금 AxB) at t-1 at t=1 (1) A X 4P

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Q: 0.6 14. Estimate g (t) dt using a left-hand sum with n = 4.

A: As you have asked more than one question without mentioning which one to do, I am solving first…

Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: Suppose that an initial deposit of $100 is made, and a deposit of X is made at t = 2. Find X if…

A: Given that : Principal value = $100  when t = 2. Amount = $350  when t = 4 To find X = ? To use the…

Q: c) Converge by integral test Q.10) fxe-x dx = a) 6e-5-1 25 b) 1-6e-5 25 c)(4+1) 2$ -6e-s 25 d)-

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Q: Find the sum of E n(n + 1)x" = for < x </

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Q: centered at z = -1. (-1)" (n + 1)(x + 1)" n+1 E"(z + 1)" Σ n! O m-0 El-1)~ (n + 1), (x+1)" n!

A: 1. The function given is fx=1x2. At x=-1, f-1=1. Finding the derivative of the function at x=-1. The…

Q: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

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Q: During a recession, Congress decides to stimulate the economy by providing funds to hire unemployed…

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Q: Monthly sales of a particular computer are expected to decline at a rate of d(t) = −25t 2/3…

A: Let sales be s.dsdt=-25t23∫ds=-∫25t23dts=-25t23+123+1+cs=-25t5353+cs=-15t53+c

Q: 11) Internet rentals affect "k" Video in such a way that the demand for rentals of its DVDS changes…

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Q: 3.) Using an iterative such as Gauss -Seidel, solve the converged results at three decimal places.…

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Q: Given that n2 1 and xn =V 4n² + 3n – 2n Will {Xn}, be divergent or convergent? n=1 Will E-1 Xn be…

A:

Q: Suppose a survey shows that a mayoral candidate is gaining votes at a rate of 2000f + 1000 votes per…

A: A candidate is gaining votes at the rate of 2000t+1000 votes per day, where t is the number of days…

Q: How does h(n) = n2 /2n behave for large whole-number values of n? Does h(n) tend to infinity?

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Q: b) Find L[e* S (-os22) dt] and -1 4s+5 * ls-1) (s+2).

A: Laplace transferom and inverse Laplace transferom, using all the properties.

Q: A production manager determines that t months after production on a new product begins, the number…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.