@show that a) G (x,x) => Uu6) Unl) were G is green funcfion

Q: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

Q: Find a point c satisfying the conclusion of the MVT for the func y(x) = 2e* on the interval [0, 5].…

A:

Q: Grplain why Ž diverges, 27 41 even though has a finite liniit 2 t 2

A:

Q: Show that there is a solution to the following equation in the interval (2,3). (Hint: Use the…

A: Since there are two questions posted, we will answer the first question (1). If you want the second…

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

Q: 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the…

A: Given that, The function is, f(x) = 2x3 + x2 + x + 3 = 0 interval is = (-2, 0) We have to prove by…

Q: IsP2 spanned by 1 + x, x + x2,1 + x2?

A: To Show: Is P2 spanned by 1+x,  x+x2, 1+x2 ? Concept: Let V be a vector space and let S=v1, v2, v3,…

Q: nts A and B have symmetry with respect to the ) (9, 2) (х, у) %3D -) (0, 8) (x, y) =

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let a be a constant. Given that 3x In(ax)dr = el² ( 12 – 3 * (12- )- -23 find In a. 3 %3D

A:

Q: Use Newton’s method to find thezeros of ƒ(x) = 4x4 - 4x2 using the given starting values. x0 = -0.5…

A:

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: D if x,Y,2 inclepndent Variables and z function in X, Y which achieves the eguation find az…

A:

Q: By means of Lagrange interpolation foomula, prove that 0.3 | -3 where (*)R = *R %3D

A: Given :- By means of Lagrange interpolation formula, y1 = y3 - 0.3 y5 - y-3 + 0.2y-3 - y-5 where yx…

Q: 6 2, find the following. - V (gof)(x) 2√2(1-2x) X (b) the domain of (gof)(x) in interval notation −…

A:

Q: ies of z and x

A:

Q: Dis - let g: 2Z, such That Disc Prove That. 960= 2X, e, But is not suek Discrete struar Discrete…

A: Introduction: A function makes a relationship between its domain set and the range set. All the…

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: - R-{-}→R-{} defined by f(x) = Show that f: R 3x-5 2x+1 is bijective.

A: Given function is f: ℝ - -12 → ℝ--32 such that f(x) = 3x-52x+1

Q: ag show that: coth's =ţ he (xal/, X-1

A:

Q: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D

A: from above distribution is binomial  f(x)θ=θx(1-θ)1-x  ;0<x<1 E(x)= nθvar(x)=nθ(1-θ)…

Q: Determine whether Rolle's Theorem can be applied to 22 –1 f (x) on the closed interval –1, 1. If…

A:

Q: 4. Show that if A is closed in Y and Y is closed in X, then A is closed in X. Verify it and make…

A:

Q: If y = xsinx then prove that y''+y=2cosx

A:

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: Calculate x - z. (Image 24 JI 8х -2 2x +1 3z z + 22

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: Sketch a model atleast 2 axioms of Pappus's Geometry and identify those axioms

A:

Q: limf, is measurable 00 ylan ihi

A: GIVEN a statement

Q: ☺ show dhat 2) G(x,x) => Uola) Uorlo) were G is green funcfion

A:

Q: Questione Let R=7LO7L. Show that the palynomials (,0)x in R[x] has in finitely many roots.

A:

Q: 6. Show that the half open interval [0, 2) is uncountable. (Hint: We know that (0, 2) is uncount-…

A: Since the interval (0, 2) contains the infinite subset {1.2,1.3,1.4,...} So (0, 2) is either…

Q: ☺ Let (u,Ue...,un) be a lineorly ndependent list. Which True Statement? is a has --- a non-zero…

A:

Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x = (2y + 1)/…

A: Domain of a Function The domain of a function explains what values the independent variable, X, can…

Q: Dimension of ker A is Rank of A is

A:

Q: Sketch a possible function that satisfies the following conditoons: a) Quartic, as x goes to…

A: It is known that a polynomial function with n degrees has at most n zeros and n-1 turning points.…

Q: Let H = Span{1+x,1+x², 3+x +2x², 2 + x + x²}. what is dimH?

A: Solution

Q: 2. Let a,, az,.., a, be numbers. Show that there is a single number r such that foxo: (-a,) + (z –…

A: Solving

Q: A quadratic fuction f is given in photo provide

A:

Q: a) Verify Rolle's Theorem for ƒ(x)= 2.x' – 8.x + 4 over the interval [0,2].

A:

Q: Show that lGl =20 , so G is not simple

A:

Q: Let X1,..., Xn be Show that Y = min(X1,. %3D Show that

A: From the given information, X1, X2,.....,Xn are independent, Xi~expλi The density function for Xi…

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: Find the value of K that make s the funtion fcx) Continus : x*+ 3K メニ2; %3D 2K-X > 2

A:

Q: consider fixi) = %3D show that trany2 eloes net suhsty kipschifzconchition elo muiswechenclndes ino…

A: 3

Q: If f(x)=x^3/3 -3x Show that f(x) satisfies the hypothesis of the Roll's Theorem on the interval [-3,…

A: Topic:- rolls theorem

Q: (*;)-()0)

A:

Q: 7. Use the Intermediate Value Theorem (IVT) to show that there is a root of the equation In r = 3 –…

A: We can use intermidiate theorem in order to solve the given problem.

Q: Having aeR and ɛ > 0. Define ɛ-neighborhood of “a"

A: Explanation of the answer is as follows

Q: Find the linearization L(x) of f(x) at x = a. f(x) = 3square root of x, a = 27 show all work

A: fx=3x, a=27 Differentiating with respect to x, we get f/x=3·12x    ∵dxdx=12x=32x Now,…