Using appropriate methods to show that 1. 5x2 +3x-2 dr r(x+ 2)2 In a + 6 In |r + 2| + +C. (r+2)

Q: 3. Give an example of a mathematical theorem.

A: Since you have posted multiple question, we will solve the first one for you. To get the remaining…

Q: Find all integer x satisfying the condition x = gcd(4x + 3, 2x). Justify your answer.

A: To find all integer x satisfying the condition  x=gcd4x+3,2x

Q: Using Regula-Falsi method in finding the root of f(x)=x2-8 with an initial guess of [2,3], determine…

A: Using Regula-Falsi method in finding the root of function f(x)=x2-8 with an initial guess of [2,3]…

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A: We need to find x and y.

Q: Min z = 4x1 + 2x2 s.t. 3x1 + x2 ≥ 27 -x1 - x2 ≤ 21 x1 + 2x2 ≥ 30 x1 and x2 are unrestricted .

A: the given LPP is as follows Min z=4x1+2x2 subject to  3x1+x2≥27-x1-x2≤21x1+2x2≥30 where x1,x2 are…

Q: 10. Factor the polynomial 4x2 – 4x +8 into a product of irreducibles viewing it as an element of the…

A: Factor the polynomial 4x2 - 4x + 8 into a product of irreducibles viewing it as an element of the…

Q: Qi find theintervals of the hundfioAon which, imcreofing ond the istencls on which lecreasing O…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: a bijection (not the binomial theorem!), prove that for n E N Using Σ-1()- =0

A: Here we know that:

Q: Factor x^3+x+1 over Z3

A: We have to factorize the polynomial x3+x+1 over Z3. Take px=x3+x+1. Note that, Z3=0, 1, 2 and the…

Q: Using partial fraction in evaluating A 6-2x B 2x-6 © - ²7/ 1/1/2(2x + 1) = 7/7/2 Ⓒ - 1/2…

A: Given ∫3x2+7x+28x3+x2+7x

Q: ample #2 ultiply the polynomials (x – 1)(x* + x³ + x² +x+ 1) using a table. Generalize the pattern…

A: the polynomial given to us is (x-1)(x4+x3+x2+x+1) solving the brackets we get…

Q: PROVING 19. If z = x+y az show that x = 3z.

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

Q: legendre polynomial Prove that P2n(0)=(-1)n 1.3.5.7......(2n-1)/2nn!

A: For the solution of the problem follow the next step.

Q: mial x3+2x+3 EZŞ[x] product of irreducible polynomials of 75[x]- e se

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Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that3 + x – 1 =0 has exactly one real…

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Q: The polynomial P1x2  5x21x  4231x  72 has degree. It has zeros 0, 4, and . The zero 0…

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Q: Proving. 1. Show that-3XEA P(x) is equivalent to XEA¬P(x).

A: There are two quantifiers "there exist ∃" and "for all ∀". The negation of a statement p is written…

Q: express     n-1 Σ((k^2)/n) k=1   in closed form.

A: The given question is related with closed form of finite sum. Given that,…

Q: Using Bisection method to find the root of f(x)=x³-x-3 over the interval [1,2] and n=10.

A: fx=x3-x-3 First Iteration f1=13-1-3=-3<0f2=23-2-3=2>0 So, using Intermediate value theorem,…

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A:

Q: 10+ Concave up on the intervalcs): Concauc down on the intervalcsso 4- 6 There is an in flection…

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Q: Clanfl Find Z of 8 - ) 2- 2-i Z= 2-¿ 2) Z

A: As we know that, For the complex number Z=a+ib, the complex conjugate of Z is Z =a-ib. And For the…

Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: polynomial f(x) with real coefficients and leading coefficient 1 has the given zero and degree.…

A: We have to find

Q: Find an nth degree polynomial function with real coefficients satisfying the given conditions. N=4;…

A: The roots  given are 2,-12,3+3i. One of the root is complex root and the complex root occur in…

Q: 2/5+5/2 2/5-5/2 Express in the form g +rvs where q,r and s are rational numbers.

A: Simply rationalize the given expression and simplifie.

Q: Test for symmetry: 6x2 +5y* = 2 m soolaisvic tni-y d niomoc Ans 11a Determine whether f is even,…

A: 11.a The given equation is, 6x2+5y4=2. Test for symmetry: An equation is symmetric about x-axis, if…

Q: o-(2) 16. f(x) 15. f(x) = In In X 17. g(x) = (In x)4 (Hint: Use the Extended Power Rule.)

A: Extended power rule:

Q: The ELISA test is used to screen donated blood for the AIDS virus.  It is estimated that 0.5% of the…

A: GivenThe total number of bottles of donated blood =1,000,000The percentage of population infected by…

Q: 7 45 and fourth term of (3x -) 6. Find the product of expressed 2 as P.

A: The complete solutions are given below

Q: 2- Discrete dx" using polynomials with backward differencing in equisized grid. n is one before the…

A:

Q: Σ (-1)* True/False: We have = -1. (2k)! k=0

A: We know thatcos(x) = ∑k=0∞-1kx2k2k!

Q: A binomial distributinon with parameter n=5 satisfy the property 8P(X=4)= P(X=2). Find P left…

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Q: x+(x+1)+(x+2)+(x+3)+(x+4)=5x+10 What does this prove about the sum of these natural numbers?

A: The sum of the given equation is calculated as follows.

Q: (4) positive integer n is composite without actually factoring n. Then use this method to show that…

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Q: 10-If p is a prime number, then in Z[x] the polynomial x -1 –1 = a) (x - 1) (x + 2) (x –- 3)... (x +…

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Q: The Simple and General Power Rules both require that n ≠ -1. Why is this restriction necessary? What…

A: The simple and General power rule for integration is as follows: ∫xndx=xn+1n+1+C If n=-1, then the…

Q: Intro to proofs Given : AB=DC PROVE x=8 2x+5 =AB 5x-19= CD

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Q: (7- 2n)(n+ 3) 1- 2n 3n* – 11n +9 V 9n + 4n + 1

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Q: Review of the Remainder Theorem Evaluate each function at the given value 1)= a4 − 2a3 − 8a2 − 3a…

A: Remainder Theorem use to find the given value of variable is zero or factor of given polynomial or…

Q: ind the definite integcal uoing any method. 3/2 x13-2xdx

A: Follow next step

Q: ee polynomial has (n – 1) critical numbers. An nth-degree polynomial has at most (n – 1) critical…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Find all integer x satisfying the condition x gcd(4x +3, 2x). Justify your answer. %3D

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Q: 2.2 INTEGRATION OF RATIONAL FRACTIONS 16

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Q: general conclusions :25. Given X ~ N(µx, ox), prove that X~ N(Hx, ox/n). Hint: var (X) = + X ").…

A: Given that X~Nμx,σx2 Consider, E(X¯)=EX1+X2+.....+Xnn       =1nE(X1)+E(X2)+.....+E(Xn)…

Q: ind the general solution using Reduction of Order:

A: The given differential equation is: y''=2lnx Let y'=u so y''=u'

Q: 28. Graph of f" 2+ -1 2 3 4 5 +x+ 5 -4 4- 5. test to determine the local 2.

A: Graph