Prove that 1 1 16 ≤ (a+b+c+d) = + = + b + ax (²=²+ + + + + + + ² + 1 = 0) d for all positive numbers a, b, c, d.

Q: Suppose, X|0~ Binom(m,0)and 0~ Beta( a,B), then E(X) is equals to, а) тав b) aß ma c) a+ B me d)

A: Given: Suppose,  Xθ~Binom(m,θ) and θ~Beta(α,β)

Q: Use the Chain Rule to compute In(u² +uv). au

A:

Q: 9) 444 (11) Evaluate the following integral; A) 4 Injx-21-In/x+3/+C C) 4 In/x-31-In/x+2)+C B)…

A: Here we can use method of partial fractions to find the required integral. We also need the…

Q: 2. Prove the general formulas (GF)» = G«F* and (F-')» = (F«)- in the special case where F and G are…

A: Given G and F re isometries in ℝ3 To prove  1.GF*=G*F*2. F-1*=F*-1 Since F and G are isometries in…

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b>0. Then there…

Q: (b) 3x + 2 in Z,[x]

A: Given that 3x+2 in ℤ7x. We have to find all associates of 3x+2 in ℤ7x.

Q: (Q-3) function y=fG. This stretch bu a factor of 3 units. 1) Point (2-3) is a point 15 A gpint…

A: The given function is: y =  f(x) (2, -3) is a point on the given graph.

Q: 5. Fuind the mat aut ward fluse lof the field , (F) the foundang of the regian , and s(x, y,x) =…

A: The general form of a vector valued function in three dimensions is given by , where , and are the…

Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

A:

Q: 3. Give an example of an orthonormal set with 4 non-trivial vectors in R5.

A: We have to solve given problem:

Q: Determine whether each statement is true or false   (a) A ∩ A'= φ (b) If A ⊆ B, then A ∩ B = B.…

A: Explanation of the solution is given below...

Q: @ (3.+j4)*

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: to Prove that : Ge = { in (+ + ² ) Z tan z =

A:

Q: 2. Prove the general formulas (GF)* = G*F* and (F')* = (F*)' in the special case where F and G are…

A: An isometry in R3 is a one-one onto function which preserves distance that is for a ∈R3and b ∈R3…

Q: Find the set of ordered pairs (T0, Yo) for which Picard's Theorem guarantees that the IVP y ry %3D y…

A: Given,            y'=xyx+y, y(x0)=y0

Q: Let 1 2 A = 3 6 Is A invertible? Explain your answer.

A: To verify is the given matrix A is invertible Or not.

Q: a) Use Backward difference to find the Finite difference equation of the follow ди ди o'u -= C- xe…

A: We are given the equation ∂u∂t+a∂u∂x=c∂u2∂x2 , x∈ 0 , 1  , t≥0 Let us consider a grid of points in…

Q: Prove that if A is invertible, then 1 det (4) det (4-¹) = -

A: We have given that a square matrix A is invertible. To show that detA-1=1detA. We know that an…

Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

Q: 3 Compute the primitive of w= (z³ - x² z)dx ^dy - x²dx ^ dz + (3y² z - 3xz²)dy ^ dz

A: The primitive of a differential form is also known as its antiderivative. In this case, we want to…

Q: We proved the following theorems in previous group work. Write the dual of each of the theorems and…

A: To find- Write the dual of each of the theorems and prove that each dual statement is true. A ∩ B ∩…

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: Evaluate Laplace of [9e^-5t + 2e^3t + 6t^3 - 10]

A:

Q: Find a basis for span(sin2x, cos2x, cos 2x) in F

A:

Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: 1う× ) did Fis erimitive af F af F 2) did p is integrable

A:

Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t>0=0, t<0 Therefore,…

Q: PROVE THE STATEMENT "There exists a, b ∈ Z+, such that if a > 1 and b > 1, then gcd(a, b) > gcd(a^3,…

A: Given statement is wrong because there is no a, b ∈ Z+, such that if a > 1 and b > 1, then…

Q: Find the norm of (-4,- 1/4,3, 1/3) belong to R^4 w.r.t the Euclidean Inner Product on R^4.

A:

Q: Show that given that z = sin-12 дхду дудх

A:

Q: To prove L'Hopital's Rule for the case, you use what Theorem and what statement is a direct result…

A: For ∞∞ case, we can use the l'Hospital rule by taking the derivatives of numerator and denominator…

Q: B\ If X is Pre-Hilbert space then (x,ŻB,Y, ) = ΣP, (x,y, (x, j=1 j=1

A:

Q: Use the inner product (A,B) = 2a11b11 + a21b21 + a12b12 + 2a22b22 to find (A, B) for 0 A - [27][221]…

A: Given A = 1-124,   B = 01-20

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: If l is a line through (0,0), the point (0,0) divides the line l into two rays. Also, a…

A: To determine for which rays starting at the origin ez is bounded, we need to analyze the behavior of…

Q: Prove or disprove the following statement: A) Every T'3-space is T4-space?( explain your answer)

A: The statement "Every T3-space is a T4-space" is true. To understand why, let's first define the…

Q: brichingen. dingena determine the Convergence or of N= 1

A: The given series is ∑n=1∞e3nnn

Q: How can we prove to get dual from primal standard form? from this primal standard form Max.z = c'x…

A:

Q: 3) if Aza,i + a₂j + a³k , 13 = bi + bj + bk Prove that the .(A-B) -13 -(DXA) - A - (DXB) Vactors

A: We have to show Note: In the question  is given which is incorrect. It should be

Q: flx) = x (x-2)+g Eメとス ;if x22 Show that there exists a S such +hat 1x-2166 implies fex)-8<A

A:

Q: Prove that the dual of l' is isometric to 10⁰.

A: Accounting to the given data, prove the given statement:

Q: (3+i)"=2" cis - пл

A: Use the  De Moivre's theorem and simplify to prove the above expression.