2) of Ec, 4" is convngend can we conclude that coch of these are comvergent: (4)

Q: - а, ь, с € R CER polynor = x° + ax

A: f(x)=x3 +ax2 +bx+c0=-23 +4a-b+c0=-8+4a-2b+c4a-2b+c=8

Q: Show that the mogping LiPaRI-+IR L Carcaxtat = (asta, on) is liher trasfaret

A:

Q: what

A:

Q: Show that (A, <) is a poset. (Hint: While showing antisymmetry and transitivity, you may need to…

A: As per guidelines, we will solve first question only. Given A=1,2,3,4,6,8,9,12. Consider a relation…

Q: Let x = {1,2, 3, 4} and P= { {},{2,3} , {43} - っ- %3D nd

A: X=1,2,3,4P=1,2,3,4

Q: 3. Prove that sinOtcos=1.

A:

Q: 15, If neZ, then nº +3n +4 is even. (Try cases.) ho bn 6. If two integono

A:

Q: 2. Assign Hermit's interpokting tolynomial by The fallowingy da ta:

A: The Hermite's interpolation polynomial is H(x)=∑ui(x)⋅yi+∑vi(x)⋅yi'. Here…

Q: 2. Show that In (- - ) = ( + 2nn)i where n = | .... .... ..

A: Consider the following expression: x=ln-12-32iex=-12-32icosx+isinx=-12-32i

Q: Prove using the IVT,  √2 exists.

A: To prove using IVT, 2 exists.

Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

A:

Q: Integrate  sinnuelog(cosu) . Where n=744

A:

Q: (i) (Z- Q) and specified in it using the most concise notati

A: Firstly we write elements of both sets Z and Q and then find Z–Q

Q: 2)Give of a homogeneous syatem of equatians with 2 equations and 2 unknoan's. 3), Why is cury…

A: 2) Take the system of homogeneous equations            x+y=0          x+2y=0

Q: 1> =a,-4,57is to U=2,-4,5 812.Detemmine -> onthogonal

A:

Q: 11. Let SC R and suppose that s := sup S belongs to S. If u ¢ S, show that sup(SU {u}) = supfs*, 4).

A:

Q: 1. Le that if same lin 2. Co converg

A:

Q: 37 17 Squeceze theorem to 8how an= 3" Conuerqcnt, Use aveeze

A:

Q: Which condition would prove AJKL ~ AXYZ?

A: Here we have to find the ratio between two sides such that the given 2 triangles will become…

Q: What statement is missing from the 2-column proof proving that ΔRUS≅ΔSVT?

A:

Q: Prove 2- = =4 has infinite many Solu thans ZEC.

A:

Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

A:

Q: 23. Find de V100- tan O coton 2 Opbon 1

A: We have the given integral as ∫dx100-9x2 On solving the given integral furthermore, we get the…

Q: If |z|=1,show that (z^-1) =(z congegate)

A: Given z=1 We have to show that z−1=z¯ Since, z=1 ⇒z2=1 We know that z2=zz¯

Q: 2. Prove ΣΫ; = Y 3 Prono ΓΥΠ |

A: Let X be a Random variable with a Probability density function or probability mass function f(x)…

Q: 1 ient of in al</z] <2 is

A:

Q: Prove VEN+, 5+ 3n ≥ 22n+1

A: Introduction: The idea of mathematical induction aids in the proof of mathematical conclusions and…

Q: A, Az, An are independert,2) PLiln)=r9)-1), where Bi is eitler Ai or Ai for izlityn in please proof…

A:

Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

A:

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: EX Find theno of letter strings of length H that contain the letter y exactly 3-himes and contain…

A: Total number of letters = 26 Letter y can occur only thrice. Letters m,b,t,k can occur only once.…

Q: Supplemer 5) 90° Supplement of 90° = %3D B) State whether the given pairs are supples 1) 24°, 156°

A: We have to find the supplement of 90°  And state whether the Given pairs are supplement. 24° , 156°

Q: 13 is discret coply on asetR Shotr the t Ris dines th Ror not

A:

Q: 火2sin C&) for ダチo fcx) = { for x =0 show that Con tinods or not

A:

Q: true or false without justify The sel { 1,2,t, 3,,4,+, csx, coss is mot Ti Bomded in (CToi], Ul6)…

A: True.

Q: 2. is it or divery Con

A: To solve the problem and find its convergence

Q: 2 FIND THE PARAMTRIC AND SYMMETRI C EGUATIUNS OF THE LINE THAT PASSES THROUGH (2,8,10) AND く2,8,147…

A: The given data is: The line passes through 2,8,10 and parallels to 2,8,14 To find the parametric and…

Q: 3 has infinitely many soluti

A:

Q: 81: Without evaluoting, show directly * = ? satiefy 2. %3D 2 -5

A:

Q: Let A=(aij)nxn be symmetric and positive definite. Show that laul< (anan), , lis = 1,2,..n 9

A: Given: Let us consider the given, A=aijn×n Let's prove that aij&lt;aiiajj12,i,j=1,2,...,n.

Q: About proportionsIf a/b = c/d and r/s = m/n , form a single proportion involving the eight…

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

Q: Give 5 examples of Postulate and Theorem using own words, based on rea-life experiences. Do this in…

A: Postulate: A postulate is a statement that is assumed true without any proof. Theorem: A theorem is…

Q: These are separate quesitons

A: a) At x = 2, f(2) lies in the fourth quadrant where y is negative. So f(2) is negativeb) From the…

Q: 6. Show that Autoq(Q[3], 5]) is finite.

A: To show: Autℚℚ35,53 is finite.

Q: 3. prove that: det (AB) det (A) det (B) If A -(:), = - ( :) B = 7 2

A:

Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? What is the smallest…

A: It is given that p and q are prime numbers. Assume that gcdp, q=d. Then, d is the greatest common…

Q: what expressi on is equivaient to this. (n-a)!

A: n!(n-2)!+n=n×(n-1)×(n-2)!(n-2)!+n  [we use the idea of factorial]=n(n-1)+n=n2-n+n  [distribute n]=n2

Q: Is f(x, y, z) = 8 In x+7 In y+5 In z homothetic? Of(x, y, z) is not homothetic Of(x, y, z) is…

A:

Q: 10- Prove that a.b3D la+bl2- la-bl? /4

A: Prove that a.b= la+bl²- la-bl²/4

Q: the Fucdidean <41s open in is Me toie on CA) Trul False Please gine auswer with explaination

A: Euclidian Metric : The Euclidean distance between points p and q is the length of the line segment…

Statements and Logic

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