THEOREM 23. Let K be an integral operator on L2([a, b], a) KS = [°xe K(x, y)f(y) da(y) where T| K(x, 9)* da(+) du(y) < co. Then K is a compact operator.

Q: 6. Theorem 131

A: The figure of the circle is given by Theorem : ∠Q = 12mPSR⏜ - mPR⏜ To evaluate : The value of ∠Q

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

A:

Q: a (1, 0, 1), b = (2, 1, −1) and c = (1, -1, 4). Calculate |ax (b+c)].

A:

Q: C_A* UI

A:

Q: What are the complete ordinates for simpson's rule?

A: Simpson's rule is given by ∫abf(x)dx=h2fx0+4fx1+2fx2+...+4fxn-1+fxnWhere,xi=a+ih

Q: b) Show that z, + z, = z, + Z, . 2

A:

Q: Prove that (x - i) = > xi i=1

A: We will prove the following result.

Q: at II Prove that if a;-ta and b;→ aj + q sa+b. →a and b.

A: See the attachment

Q: What does the Theorem of Pappus say?

A:

Q: Hiw- prove that %3D

A:

Q: prove that div A マ - Kr

A:

Q: Evaluate W(1 + x, x, x^2

A:

Q: Compute 1 $ Jzmi\mu (22 +4)24z

A:

Q: Is (2,1)=(1,2)?

A: The objective is to determine whether 2,1=1,2.

Q: dz

A: Wallis FromulaFor  positive integer n∫0π2sinn x dx=∫0π2cosn x dx       If n is even   1.3.5. ...…

Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

A:

Q: 1 Ita Į = ab

A: The objective is to show that, 11111+a1111+b=ab

Q: find powerset of A = {0, 0, 1}

A:

Q: Evaluate iy ( + + " ). Nin t

A:

Q: verify that (AB)T = BTAT

A: Given matrices: Now,

Q: State Green’s Theorem

A:

Q: ! = [2, 2, 4, 2, 2] =

A: Just notice the method of writing denominators carefully.

Q: State and Prove Pick’s Theorem.

A: Let P⊂ℝ2 be a polygon with all vertices on lattice points on the grid Z2. Let  I be the number of…

Q: A2

A: Consider the matrix A is, A=0100 Apply the condition, A2 = O. 0100·0100=0000 The matrix A is…

Q: State and prove Littlewood's Third Principle

A: Littlewood's Third Principle, or the law of iterated logarithm, can be understood intuitively as…

Q: What are all of the theorems used in a ferris wheel?

A: A Ferris wheel is a type of amusement attraction that consists of a revolving upright wheel with…