1. Classify the following series: a. 7, 9, 11, 13...... b. n+2, -2n - 4, 4n+8.........

Q: ∞ 3. Define rN=S-SN= Σ n. Show that Σ n=N+1 n=0 Zn = s if and only if lim || = 0. N→∞

A: Please refer below page.If you have any doubts please feel free to ask.Explanation:Step 1:

Q: Find two sets A and B such that A E B and AB.

A: A=ϕ. And B={ϕ}Explanation:If you have any problem let me know here in comment box for this thankyou.

Q: In 2018, Singapore's average income was $64,581.95 US dollars. The exchange rate was 1.35 per US…

A: The objective of this question is to convert the average income of a person in Singapore from US…

Q: Suppose the variance of X is 14. What is the variance of .47X?

A: The objective of this question is to find the variance of a random variable that has been scaled by…

Q: We assume that in a village there are farmers, carpenters, and tailors, who provide the three…

A: Let's denote the total production of food, housing, and clothing by farmers, carpenters, and tailors…

Q: Let \( g \) be a bounded function on [0,1] and assume that the restriction of \( g \) to the…

A: Below solution was explained in detail.by carefully choosing a partition and utilizing the…

Q: The legislature in a state has 49 seats. Apportion these seats to the five counties below using the…

A: Given Information:The legislature in a state has 49 seats.The seats is filled across 5 countries.The…

Q: 3. Determine Domain, Range and graph of the following rational function f(x) = 1 -3x+1 +2

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Q: The Solomon Islands has average precipitation of 3028 mm per year. On a random week in Solomon…

A: The objective of this question is to calculate the expected rainfall in the Solomon Islands in…

Q: Determine whether the statement is true or false. Prove the statement directly from the definitions…

A: a. For all integers a,b, and c, if a | bc, then a | b or a | c.To demonstrate this assertion, we'll…

Q: 5. Given (1-1)y+ty' - y =0. Show {t, e'} forms a fundamental set of solutions to the above…

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Q: Determine whether the given graphs have an Euler circuit. Construct such a circuit when one exists.…

A: The given graphs are drawn as follows.(a)(b)We know that an Euler path is a path that passes through…

Q: Can you break these 3 questions down in a step by step so I can understand. 1. Find two sets A and B…

A: Explaning line by lineExplanation:

Q: 4. Calculate Res z+1 z²+9 -3i

A: The answer is (1/2)+(i/6)Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Does the graph below has a Hamiliton Path? If so, find such a path. If it does not, give an argument…

A: The objective is to find a Hamiltonian path.

Q: Find the general solution of the given second order differential equation. 3y'' + 2y' + y = 0

A: The objective of the question is to find the general solution of the given second order homogeneous…

Q: 17. Find by separation of variables the ordinary differential equations following partial…

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Q: Using Fermat's little theorem, find the least residue of the (multiplicative) inverse of modulo 877.…

A: We need to find the least residue of the (multiplicative) inverse of  modulo .We know that, Fermat's…

Q: Find a general solution to the differential equation. 1 -e 4 1 "y" +6y=2 tan 6t-

A: Given, a second-order linear linear ordinary differential equation.It is required to find a general…

Q: Use the method of variation of parameters to find a particular solution of the following…

A:

Q: Consider the following. My recent marketing idea, the Miracle Algae Growing Kit, has been remarkably…

A: Dear student, kindly check the answer in the explanation box below.Explanation:Part 1: Answer:The…

Q: 4. y = sin 2x 1-cos 2x

A: We have to find the derivative of

Q: Suppose that Var(X) = 934.93, Var(Y) = 11297.02, and Cov(X,Y) = 2912.35. What is Var(.87X + .13Y)?

A: The given .The aim is to find the .The formula used .

Q: 3. Calculate Res e² - 1 ¹1:0). Z

A: Res( z(ez−1)​; 0) = 0.Explanation:It looks like you're asking for the residue of the function…

Q: Suppose the relationship between Y and X is given by: Y = 51 + 6X By how much does Y change if X…

A: The objective of the question is to determine the change in the value of Y when X increases by 1…

Q: Guess a formula for 1+3+5+...+ (2n-1) for n ≥ 1 and prove your result by induction.

A:

Q: Consider a random graph G(N, p) with e² In 2 3N 3/2 р = .In the limit N → ∞ the average degree (k)…

A: The objective of the question is to determine the average degree (k) of a random graph G(N, p) in…

Q: Let 1, 2, y be decision variables, 91 (1, 2) and 92 (1, 2) linear functions, and b₁ < 100 and b2200…

A: Let  be decision varables.  and  are linear functions. are input parameters.The given constraints…

Q: In a harbour, there are 2 landing places. Ships arrive at a rate of 8 per day (exponentially…

A: The arrival rate of ship =8 per dayLoad or unload rate of the ship The profit made by the company…

Q: Let A = 16 -28 0 -28 53 10 0 10 29 a) Prove that A is a positive definite matrix. b) Find the…

A: (.). Given matrix is,           (.) Necessary and sufficient condition for positive definite matrix:…

Q: Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c)…

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Q: Give an example of a relation on the set A = {1, 2, 3, 4, 5} that is a) both symmetric and…

A: The set The aim is to give an example of a relation on the set A that is a) Both symmetric and…

Q: : 8. Solve the differential equation: y' - 8y' + 16y= 16e²*, subject to y(0) = 0 and y(0) = 0. Using…

A: We are to solve the differential equation using variation of parameter method subject to y(0) = 0 ,…

Q: The variance of temperatures (Fahrenheit) in Denver, Colo. is 328.87. What is this variance if temp…

A: The objective of this question is to convert the variance of temperatures from Fahrenheit to…

Q: Consider a Poisson random graph of average degree c = 100. You observe a node with a 500. How many…

A: The objective of this question is to determine how many standard deviations the observed degree of a…

Q: 2. Solve the following Bernoulli equation: xy' = y - xexy²

A: Given differential equation is    This can be written as      Substitute, , then we get   Thus,…

Q: Let a, b, and c be integers with a 0. Prove that if a | b and a | (b + c), then a | c.

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Q: 15. Calculate the Fourier series in sines of the function f(t) = t³ in the interval [0]

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Q: 28. Show that if A C C and BCD, then AX BC CXD

A: Below complete solution is Given.Explanation:

Q: Write the level surface 4 = 2x² + 5y + √√z as the graph of a function f(x, y).

A: Given, an equation:It is required to express the level surface as the graph of a function , meaning…

Q: Given a relation g from the set D = {1, 2, 3, 4} to the set C = {a, b, c, d} where g= {(1, a), (2,…

A: A relation  from the set  to the set  where .The objective is to determine whether the relation is a…

Q: Suppose Var(X) = 32, Var(Y) = 47, and X and Y are independent. What is Var(.15X + .85Y)?

A: Given, a  and .And that and  are independent.It is required to find the .To solve this problem, use…

Q: 1. (a) Construct the first Taylor approximant to f: (−1,1) → R, ƒ(x) = sin¯¹ x about a = 11. (b) Use…

A:

Q: 4. Find the solution of the initial value problem y"+y'-2y = 0, y(0) = 0, y'(0)=1.

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Q: Do the following with the given information. S² 17 cos(x²) dx (a) Find the approximations Tg and Mg…

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Q: Let ← || 8 N -6 Plane 2 and V₂ = 12 3 -9 then the geometric description of Span {V₁,V₂ } is A set of…

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Q: 6. Obtain the value of x from the following equations a) 67-* = 62x+1 b) log₂ (x²)- log₂ (x - 2) = 3

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Q: Verify that the given differential equation is exact; then solve it. (9x² + 7y²) dx + (14xy+9y²) dy…

A: Given differential equation is .We have to verify that the given differential equation is exact and…

Q: Suppose the avg score on Midt1 is usually 95, and on Midt2 is 75. If your final grade is weighted…

A: The objective of this question is to calculate the expected final course grade given the average…

Q: The average value of a function f(x, y, z) over a solid region E is defined to be 1 fave (E) . f (x,…

A: