9. Let S- {xeZ| 3r.seZ,x=9r+6s) and T={xeZ| 3x} b) Prove that T Cs. a) Prove that SCT. Hint for (b): 9n + 6(-n)= 3n

Q: 3. Evaluate || (3y+ 2x“) dA, where R = {(x, y) E R² : |x|+|y| < 1}. R.

A:

Q: HW 2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 <Z< 2) c) p(-2 <Z < 1)

A: If Z~ N(0,1)   which means clearly it is standardized normal distribution table.

Q: i) (i x j).k = 2.

A:

Q: 2x-1 Find f1) if Az) = %3D x+2. a) O b) O c) O d) 515

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Q: C. Prove that B,(f)² < Bn(f²). HINT: Expand B,((f – a²).

A: Given: Let's prove the given Bnf2≤Bnf2.

Q: If z = 3x2 – 2y3, x = 1+ s²t and y = 33 – t2, then dz %3D O a) 6x(1+ s²)+ 12ty O b) 6s²x – 12ty - c)…

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Q: Submit through Canvas as indicated. T u = (2,-5) and v= −3i+7j

A:

Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

Q: Expond lap(cora) in powers of (x-2) wing Taylon's Thusem

A: The given function is: f(x)=log(cos x) To expand the function using Taylor series around a=2 using…

Q: Q3: If P(X= x) = a 8(x) + b 8(x + 1); then a + b = A) 0.5 B) 0.3 C) 0.4 D) 1 E) None

A: Given: P(X=x)=aδ(x)+bδ(x+1)

Q: 4 Lonsider the functlan fx)= -5x4- |l+x?tx-17. functfon Fex)= -5xH-|l+x²+2x-17. 5xH-113+ Whatis r n…

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Q: Determine whether (p→q)→(q→r) is equivalent to q→r. Justifyyour claim.

A: we have to check whether  (p→q)→(q→r) is equivalent to q→r

Q: best Rank 2 approximation F ind weth respect to I|F|l the where to A -1 2 -1

A:

Q: Let B = {1-3t +t² , 2 - 5t + 3t2, 1 + 5t2} and p (t) = 2 – 5t + 4t. Find x [p]g. %3D X1 = X2 = X3 =…

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Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

A:

Q: 6.- Evaluate T(au + bữ), considering the following 1 T(ī) = 2, T(5) = , T(ī) 2, a = -1 and b = 2 3…

A: T(au+bv)=T(au)+T(bv)

Q: dx бх3 + 2x2 + Зх dx = Q(x)/x² + 1+ a Vx2 + 1 Vx² + 1 What is the value of Q(1).1

A: The given integral is: I=∫6x3+2x2+3xx2+1 dx

Q: V(12r), v°(-8r)

A:

Q: Find the difference quotient, a) 5h²+2a+h+6 h Ob) 10a + 5h + 1 O c) 10a +1 Od) 5h + 1 f(a+h)-f(a) h…

A:

Q: Prove from the definition: n3 + 65n2 + √n = Θ(n3)

A:

Q: 6e dz by residue theorem, where C is the contour |2| = 2 Evaluate 524 + 25z

A:

Q: prove it q² + b ² + c ² = 4√30 (weit zenböck's inequility/

A: The given inequality is Weitzenbock's inequality. a2+b2+c2≥43∆

Q: 13A) Find m/VWX 10x+14 4x + 21 15,

A:

Q: Prove that bx q = b. ((Vt) - Vt), where q = V x t

A: We have to prove b→×q→=b→·∇t→Tr-∇t→ for q→=∇×t→ b→×q→=b→×∇×t→          =b→×∑i^∂∂ti×t→…

Q: es (or+.1). COS Using P, (x), eshimate cas

A: In the question it is provided a function fi=cosπ+i The objective is to estimate the above function…

Q: 25) Which notation describes the translation of the sailboat B(70, 20) to the lighthouse B'(10, 80)…

A: Given: B70,20, B'10,80 For reaching from point B to point B', we have to use operation x,y⇒x-60,…

Q: Given R = a) b) 24 15 and S = 2STR 5R+S-(2STR)T 1 3 15 Find

A:

Q: 19 a) Edur 1+2r 1 b) (1 +25), | E dr

A: We will solve  the integration.

Q: 2) Let T [ ] = DT [₁2 i] = i) 0 ii) 2T = 1 + (-c-d)x+ (-d)²x² + (a + c)³ x³. Then we have: -7 - =

A:

Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

A:

Q: let x be have P.dif 0 < x <3 f(x)= ={th find The U.b. of P(IX-M73) and find The L. b.

A: Please see below

Q: ) find w=4 +iv if the function. in term of 2 is f(z) = (Z-32²) (2z+i)

A:

Q: Need c) only use product rule 3. Differentiate. a) M(u) = (1– 4u²)(u+2) b) g(x)= (-x+ 3)(x- 10) c)…

A:

Q: Cietni let ane let G4)= ti t2+34)j +4K HIC4) = 2,4し + 34j+(-144)1k fnd の) H4)XG(H) b) G4). HG4)

A: Given: Gt=ti+2+3tj+4kHt=2ti+3tj+-1+2tk

Q: 4n Prove supz : nE N

A:

Q: IF| = r r) = -i = 5xi + 2yj – 2zk so be it where div() , grad(f find all of

A: Solution:

Q: sin-¹ x = sin , prove z +Zxx = 0.

A: Given x = sin-1(z/y)  We have to prove,  z + zxx = 0

Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: Prove: for n > 1, F; – Fn+1 Fn-1 = (-1)".

A: F_n are the Fibonacci numbers which are defined by F_0=1,F_1=1 and F_n = F_{n-1}+F_{n-2} for…