9 (b) For cach E70, there exists rational number re(U, E).

Q: 2. (a) Find integers a, m, n such that m | a and n | a, but mn /a.

A: .

Q: Consider 2x° – 3y? = 8 -

A: SolutionStep I :  2x3 - 3y2 = 8Now, 2x3-3y2=8⇒2x3-8 = 3y2ddx2x3-8 = ddx3y26x2 =…

Q: 13. Suppose that p + q = 25 and px q = 10. Determine the value of of +2+1+1/2+2 32 10 41 20 (A) (B)…

A: Here we have to find the value of the expression.

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

Q: 5. Let x and y be real numbers and x 0. Prove the following 1 "If x and 3 are rational, then X is…

A: Let x and y be real numbers and x ≠ 0. Let, x and y/3 are rational numbers.  then by definition of…

Q: Fix a € (0, 1). Determine inf(B) for B = {an: ne N}. You can just give your answer for this part…

A: We have to find the  for

Q: What is the exact value of csc > O 2√5 3 IN O-2 14 (¹4) ²

A:

Q: Prove that if x is a rational number andy is an irrational number, then x + y is an irrational…

A: As you have asked the problem ( b) only. I have solved this problem in two steps by showing the…

Q: 2. The set of all rational numbers in the interval (0, 1).

A:

Q: 00 8tan-in Zn=1 n3D1 1+n2

A:

Q: y = nedir? (a) (b) (c) (d) (e) In(x² - 4) tan-¹ (²-1) fonksiyonunun tanım kümesi (-∞, -2) U (2, 3) U…

A:

Q: 7. I) Find, if possible, AB ond BA A= 3212/ 2.

A:

Q: How make that? k = (5²+1) JK ds = (5+1-15+0·1) ·10 (115²-185-11) (105²+115+1)²

A: Step 1: Given K=−(s2+1.1s+0.1)(s2+1)​. To Find: dsdK​ Step 2: We know that if f(x)=v(x)u(x)​, then…

Q: Show that 3 € Q| /6|.

A: Given  ℚ6=a+b6:a,b∈ℚ  To prove : 3∉ℚ6

Q: 2 Find (5a" + 4a*) da 1

A: We can find the integration value as below

Q: Find k such that, 2 det 4 li0 -8 -5] -1 -7 = 510 k 0 .

A: Given det2-8-54-1-710k0 =510 we have to find k

Q: 2 We know that & is clased under "+" and Moreover,we know that ヒnaw +hut B ER-8 and (5 ER-Q. Prove…

A: Given that3∈R-Q and 5∈R-Q Have to prove 3+5∈R is not a rational number.

Q: 2 the ratio of the sum of m and n terms of an AP is m*:n“ ,show th " is (2m – 1):(2n – 1) th that…

A:

Q: 43. Show that there cannot exist rational numbers a, b such that V3 = a+b/2.

A:

Q: 1. Find L-'[l/(p² + a?)²] by convolution.

A: Let 1p2+a22=1p2+a2p2+a2=1p2+a2p2+a2= FpGp      Then ft=gt=sinata

Q: If x ER, x > 0 and r, s are rational numbers, then (i) x > 0; (ii) for x > 1, x" <xs if r < s

A:

Q: Fill in the blank. (Enter your answer in terms of t.) 1 2 + 2_2 -

A: To find the given inverse Laplace transformation we shall use the following rules 1.   L-11s2+a2=sin…

Q: Show that E(r(r + 1) =- n(n + 1)(n + 2), n E N.

A: We have to show that ∑r=1n(r(r+1))=13n(n+1)(n+2)           ∀n∈ℕ

Q: Which of the following is true? Select one: a. (n+1)= n(n) for any real number b. г(n) = n(n+1) for…

A: The objective of the question is to determine which of the given mathematical statements is true.

Q: 13D 43. If a > 1 and b < 0, then 1-101 (A) (B) 1 9 (a) (D) b(a+1) (E)

A:

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

A:

Q: (:)? /3 9. Which of the following is equal to (b) (–1)"-12·5., 3"n! 3.5-7..... (2n + 1) (Зп — 4)…

A:

Q: How do I prove that if a,b are rational numbers, then so is (a+b)/2

A: If a,b are two rational numbers, then we have to prove thata+b2 is also a rational number.

Q: Which choice gives an example that supports the conjecture, and a counterexample that nows the…

A:

Q: dx none of the choices In( + 2e) – In(e + 1) + 1 In( + e) - In(e + 1) + 3 In( + e) – In(e + 1) + 1…

A:

Q: - ₂ F₁ (-m. a + m;c; x) = +++(c + m) -r (c) dm [x²+m-¹ (1-x)²-c+m] m

A:

Q: only rational numbers?

A: ANSWER A  IS CORRECT.

Q: Find the total number of in H.C.F. of n and 36 is 1.

A: