(2). By Contrapositive: “V n e Z, if 3| (n² + 1), then 3 ł (2n² + 1)."

Q: pany 2 = 355 3.24 = 0.52 on about these two co

A: The null and alternative hypothesis is as follows: Given: As the population standard deviation is…

Q: Q.2. Proof that V= u8--

A:

Q: 8. Provide justification for you what will appear on the ex asked. (-1)" (2n)! (a) n=1 n4 – 4n -

A:

Q: Find b fa@ dk and if if x iN rofional ニ :X if x is irrational if x is rationa l if a is irretional り

A:

Q: b) Suppone that the fuel accounds 60%0 of H hee tof rock et mast of fuer To the velocuty of the…

A:

Q: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

A:

Q: If сх 3D су (тod n) and c >0 then а) х 3Dу (тоd сп) Ь) х%3D у (тod n) с) хну (тod") а) None of thes-

A: We have to solve given problem:

Q: Let z 2ev Then: 8z 8z dy sissis

A:

Q: 9b of sido s8 Into4 gnggit EGcops otivostnsliM If ((h IR>R such that h(x) =x-6) and (g R --63-70000R…

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Q: -145 2. find least 0అ కావులి Sంఖనాుంది spcave Axz b A z] 1 -4 1 1 2. 2. enter xas a Coloumn ve

A: Given that, AX=b A=1-4010012-1121,   b=3134 The least square solution to the system AX=b is the…

Q: Ave the following fancEions contindous FCx)sメーZ メー2 てト=メ 1P 2) FCX)s X 3-5X +7

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Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: Q3: Prove that (9":n e Z) (3":ne Z) but (9":n E Z) (3":n E Z).

A: We have to prove that 9n:n∈ℤ⊆3n:n∈ℤ but 9n:n∈ℤ≠3n:n∈ℤ

Q: Σ n=1 5n Vn3 +1

A:

Q: In(1 + s) - Σ-1 , for |2| < 1 because n +1 E(-1)*z* for |2|< 1. R=0 R=0 True False

A: From the given series we have to solve true/false problem.

Q: - such that n >r > 1, (n – 1)! r!(n – 1 – r) n! r!(n – r)! n - r -

A:

Q: Q.2) Evaluate cln 7 cln 2 cln 5 e(z+y+3) dzdydr In 6 In 4

A: Given triple integral is ∫ln6 ln7∫0ln2∫ln4ln5 ex+y+z dz dy dx   Note:- ex+y+z =ex ey ez

Q: 2 Delermire if fW=x s is even, odd neither.

A: As we know that a function f(x) will be  1. even function if f(x)=f(-x)  2. Odd function if…

Q: Q D 2. Identify the missing information necessary to prove that TV 1 SU S O <SVT ZUVT O ST SV ST UT…

A: Given:     Triangle Figures is given

Q: Q3: Prove that (9":n e Z} S {3":n Ee Z} but {9":n e Z} (3":n E Z}.

A: To prove:  {9n:n∈ℤ} ⊆{3n:n∈ℤ} but {9n:n∈ℤ} ≠{3n:n∈ℤ}

Q: Prove that E, k2* = (n – 1)2"+1 +2 for all n > 1. =D1

A:

Q: What is the principal argument of z = 3 + V3i?

A: Let z=x+iy be a complex number. Then, the polar form of z is given by, z=rcosθ+isinθ where…

Q: (-1)" -Σ S. n=1 Vn+1

A:

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

A:

Q: Q.8 If v = (x² + y² + z?)¯/2, prove that a2v + ду? = 0. ax2 az2

A: We find second  the partial derivatives lf given function with respect to x, y and z and then add to…

Q: a) Suppose, T(n) = 1²+2²+3²+..+n2. Show that, T(n) is in O(n³). %3D .....

A: Big-⊖Notation: Let f and g be real valued functions and assume g is eventually position. We say that…

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: (b) Prove or disprove: f: 41o → Z20, [r|10 + + r2|20 is well defined.

A:

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Employ a suitable c 2n² +3n diverge (a) V5+n² n=1

A: ∑n=1∞2n2+3n5+n5limn→∞an+1an= limn→∞2(n+1)2+3(n+1)5+(n+1)52n2+3n5+n5= limn→∞…

Q: (b) Prove or disprove: f: 41o → Z20, [7]10 → [r2|20 is well defined.

A:

Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

A:

Q: Q2-Prove tut- va" - r* ify =()()+ ()F-7 if y =

A:

Q: Encontrar el enésimo término de las sucesiones 1 2 3 4 4'9'16' 25 3n an 1 1 an (n + 1)! °n =+ (n +…

A: Consider the sequence  14,29,316,425,........

Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: 3) Ll a, = 5, Qz = 13, end Anta 5 anti - 6 an (n71). Prove by inbuetem that an =2* +3" (n. %3D =

A: The solution is given as

Q: Disprove the statement by giving counterexamples If m,n ∈ R, then |m + n| = |m| + |n|.

A: The equation is m+n=m+n.

Q: 7. f(t)=3e" cosh (In 21) -2t in two ways.

A:

Q: (3 worder fer the systew of eguations 3.0) to be cnns kut.

A:

Q: 4х +4y+23D24 2х — 4y +230 5х — 4у-52%3D 12 Q9:

A: The single point where all three planes intersect is the unique solution to the system.

Q: 2s+2 ds = In|s| – In\s + 2| + C %3D s3 +3s2+2s

A: Here, we are solving only 1st question and for the remaining question post the question again.…

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: SA (xit) = S'y St ot) SHL %3D Subject to Con d'tions Detesmine the expre ssion tor u(xst).

A: Given partial differential equation is                                 ∂∂tux, t=∂2∂x2ux, t…

Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

A:

Q: 2r+1 if the values of x, y is O none O x-1,y32 O x-2,Y3D2 O x=2, y =1 223

A: Two matrices are said to be equal matrices if they have the same order ( dimension) and the…