Which of the following rule is defined as "the sum of the first and last ordinate, twice the sum of intermediate ordinate is added. This total sum is multiplied by the interval length and half of this product"? a. Simpson's rule b. Trapezoidal rule c. Simpson's rule and Trapezoidal rule d. none of these O d O a O b

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

Q: 10) Determine if the following statements is true or false. Make sure to label your answer and show…

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Q: Q3 Prove that In Coth x 1

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Q: Use the theorems and given information to show thatr 12 3. 87 65 44- (13z- 4) * , 48 - (9z + 16), z…

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Q: 5. Find the on the interval [0, 4]

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Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

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Q: A company manufacture two different types of call phone F and E, each unit of call phone S costs (OR…

A: Given that a company manufactures two call phone F & E. Each unit of call phone F costs (OR.7)…

Q: 2. Let a € R and n € Z0. Show that of the numbers a, 2a, distance from an integer is at most 1/n.…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Suppose you are given four natural numbers w, x, y,z e N such that w>x and y > z. Show that ly – w|…

A: It is given that w, x, y, z are natural numbers such that w>x and y>z. Now we want to show…

Q: 9/State the Sufficient condition for the best apfraximation ant Prove t

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Q: of Voots of the equation. 2x+3X+5=0 is The muttiple is Ę 2. 3 Prove That The sum

A: Use the formula for the sum and product of the roots of a quadratic equation.

Q: +(X+Z) = (X+ D DE Morgar Associativ O Distributive O Commutat .... is also

A: We will solve the problem.

Q: A designer is creating various open-top boxes by cutting four equally-sized squares from the corners…

A: Given that, a square of sides x length is cut from each corner of the sheet. Then the length and…

Q: Find the null space for A. 1 8 A = -6 1 8 6 null(A) span

A: The given matrix is: A=  18-61   8 6

Q: et, a1 = 3, a2 = 4 and for n > 3,an = 2an-1 + an-2 +n², express an in terms of n. %3D

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Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A: topic - functions

Q: D. Write TRUE or FALSE on the space provided before each number. _6. x € {x, y, z} _7. x {{x}, {y},…

A: We have to check whether given statement is true or false.

Q: Now we assume that P(r) is true, that is, r can be written as a sum of 3s and 5s, for any cases,…

A: We are given a statement and its proof. We need to answer two questions about the proof. More…

Q: Show that the operation * on Q – {1}, defined by a * b = a + b – ab for all a, beQ- {1} satisfies…

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Q: Proof by contrapositive that for x, y ∈ Z, if xy is even then either x or y is even.

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Q: Let us look at all points (m, n), where m and n are nonnegative integers. Is it possible to find a…

A: We need to check the possible existence of a surjective function  f(m,n) such that…

Q: Theorem 3. Every solution of Eq.(1) is bounded if a + < 1.

A: As per the information, we will first find a recurrence relationship of the sequence, then find its…

Q: The ancient Greeks had the following definition: two lengths (positive numbers) a,b are com-…

A: (a) The negation of Pythagoras’ claim can be stated in simple terms as, “there exist at least one…

Q: 10. Determine (and explain) if the statement is true or false. (a) |{Ø}| = 0. (b) [0, 1] is…

A: Given sets is

Q: Show that yn ez, if n³+5 is odd then n is even For the toolbar, press ALT+F10 (PC) or ALT+FN+F10…

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Q: If a set E has an infimum, then it has only one infimum. Proof: Suppose that E has two infima, call…

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Q: Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

A: Consider the given inequality in the given interval. Use the graphical approach to prove the…

Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: (a) Prove the following property: (:) - (.".)

A: Hey, since there are more than two questions posted, we will answer the first question. If you want…

Q: Derive the UMVUE of h(0) = 0* where k = 1,2,...,n is a known integer. Hint: Use the interpretation…

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Q: The base of a three-dimensional figure is bound by the line y = x + 4 on the interval [-3, 1].…

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Q: Let, a1 = 3 and for n > 2, an = 2an-1 +1, express an in terms of n. %3D

A: We will find out the required expression in the term of n.

Q: (b) Let A = a + 1 and B = b+ 12. Using proof by induction, show that A+B divides An+1 + Bên+1, What…

A: here i used basic condition of divisibility and i used the notation a|b for a divides b .

Q: Pos=x-3x+e xペx (x)3D

A: First convert into simplest form and then check for discontinuity by finding left and right limits…

Q: 3 We can de fine the fallaing tunction on real mumbers ( called "absohite value") ; abs (x) = x if…

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Q: 9 show Itat Ihe maclayvin Sevies For Hense is メ+ メ t.. 4- X

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Q: Let xE [0,1] and n E N, show that the following inequality holds x2 x3 3 1+x + 2! 3! +.....+ n! (n +…

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Q: 3 and for n > 2, an = 2an-1+5, express an in terms of n. 1. Let, a1

A: The solution is given as

Q: II. Let U = R = {x € R|x° – 14x³ + 45x = J = {x €R]x² 2}. I = 아} Find the following. All infinite…

A: After solving ,  I ={-3,-√5,0,√5,3}  J= [-sqrt(6), sqrt(6)] S= (-∞, -1) u (1, ∞)  6. I n S = the…

Q: ) Evaluate, using Cauchy formula C:2- (a) zz-l dz dz (6) ( e

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Q: De langrange muitiplrers to finch three positive numbers wnosiSum is 150 and whos produt Use is…

A: Bu using the Lagrange multipliers we have to find the three positive numbers whose sum is 150 and…

Q: 1. Which property of equality allows you to conclude that the following is true? If mZD mE and mZE…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: It is easy to show thát 3 iš nót thẻ sum óf thẻ squares of 2 integers, i.e. a² +b² + 3 any integers…

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Q: Enter a counterexample for the conclusion. If x is a prime number, then x+1 is not a prime number. A…

A: Prime numbers: The numbers which are divisible by 1 and by itself. The given conclusion is that if x…

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: Nine Starbucks are located in a 3 mile by 3 mile square area in which there is a 1 mile by 1 mile…

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Q: If is a non-negative measüráble functic sa real number then Sa fx)dx = 1 Sf(x)dx E %3D

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Q: Prove that the statements are FALSE by giving counterexample each.  The sum of two odd counting…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.