(alb1 + a2b2+ --- + abnj s (af+ až+ --- + ahbf + bž+ for all ak. bk E R, ISkSn.

Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: Prove that neQ

A: Given ddxxn=nxn-1

Q: Prove that AAB = (AU B) - (An B),

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Q: 7. Remwrite the..either.five.exated.nt.agrmls. 1-X FCX ng , Z)dydzdx ZA z= 1-x2 ...... y=1-メ

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Q: Nadia would like to use the AAS Congruence Postulate to prove that ATIS = AITH. Would knowing that…

A: Given, ∠S≅∠H Also given, From the figure we get, ST≅IS

Q: Verify that (AB)T = BTAT.

A:

Q: prove that 2. catX+c

A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: Express In V16 in terms of In 2 and/or In In 16 =[ (Type an exact answer.)

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Q: Verify that det A = det B + det C, where Uj + vj U2 + v2 Uz + V3 A = A22 аз1 A32 --EE-E: A12 A22 V2…

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Q: 3. prove that: det (AB) = det (A) det (B) If a - (;). » - ( :) 2 -1 7 A = 3 2 4

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Q: Prove that S3 = Inn(S3) = Aut(S3).

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Q: Prove that no (nº.2)

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Q: Prove using the IVT,  √2 exists.

A: To prove using IVT, 2 exists.

Q: 9. Express the gcd(117,213) as a linear combination of s and t such that gcd(117,213) = 117s + 213t…

A: To write the gcd(117, 213) as a linear combination.

Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

Q: prove that div A マ - Kr

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Q: Suppise finten u ond . of U and w 45

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Q: A ball is drawn at randem fron abox Cuataining (6)red bafls(4_ white balls and (5) blue balls Find…

A: Th theory of probability has its origin in the  seventeenth century. The king of France,…

Q: Prove that %3D 3 and hence. deduce that. 3--(n+3)Jn43+ (n+s)Jnes to 2.

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

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Q: 2. and as= Determine ifb=-1 =-2 is a linear combination ofaL az

A: Follow the procedure given below.

Q: Prove %3D 11

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Q: 1/3 If (x+iy) =a+ ib, Prove that

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Q: α Let V₁ = {(₁)|a € R}. V₁ with standard V4 operations will fail both axiom "close under addition"…

A: Let A be a set and ∘ binary operation on A then 1. We say A is closed under the binary operation ∘…

Q: 28. Compute Ak where A = [4.-3] 2 - 3.

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Q: Q: Prove that tim %3D

A: We have to prove the limit

Q: 27. Prove in detail that Q(/3+ 7) = Q(/3, v7).

A: We have to prove given equation.

Q: 2. Show that 1 2 = (1 - )( - )(? y)

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Q: If A = 2x²,-3yz, xz² and qp = 2z - x³y. Evaluate A Vop and A x Vp at the point (1, -1, 1).

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Q: Prove that Vtan a de – 7//2.

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Q: Is provethat V3 is lrrational hunber

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 9. Write a 2-column proof: Given: p // q , Zg = (59 + 5x)° , %3D Za = (11x – 7)° Prove: Za = 114°…

A: Explanation of the answer is as follows

Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

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Q: 4. Prove that, VR, -11-

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Q: Find the probabiliti (a) {Y < 8 – (2|X|/3)}, and (b) {Y < 8+ (2!X\/3)}. Compare the two results.

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Q: Express E: livenr coumbination of Ÿ; = and V as a

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

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Q: Let Az = { k, k + 1, ..., k²}, for k 1,2,3, .. Find U은1Ak-nE1 Ax

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Q: Evaluate S"2 in (cscr) Szye-2dzdydx

A: Suppose a multi variable function f(x,y,z) . To evaluate the integral notice the below result :

Q: Let -{[:);}--{:)[:} -{{)}} Both B and C are bases for R2. If {x}s =: -[:], what is {x}c?

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Q: It is possible to regress x1 on y. a. True b. Falas

A: From the given dataset we have to check that , is it possible to regress X1 on Y1  or not.

Q: ,- ). Show that there a 3,4

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Q: 2 If A = 22 and B = -70 6. 10 , verify that B = s-AS, where s = -19

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Q: 4. Verify that (¹)² (j³)² = j³² | j³² but (²)³ #jj² j2

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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: Show to put nowi

A: The sample mean from a group of observations is an estimate of the population mean.

Q: 3. Suppose at a small college, 30% of the students are freshmen, and 60% of the students live on…

A: Given, The probability that the students are freshmen is pf=0.30 The probability that the students…

Q: Prove that √2+√5 is irritational

A:

Q: For what values of aand b is {u, v} an orthonormal set?

A: A set of vectors form an orthonormal set if all the vectors in the set are mutually orthogonal and…