Let f be a continuous function on an open subset U of aBanach space X into R. Let a and b be two distinct points in U such that thesegment [a, b] is contained in U and fbe differentiable at all points of [a, b]. Thenf(b)-f(a)=Df(a+0 (b-a)).(b-a),

Answered: Image /qna-images/answer/88ae1f82-04d5-4611-a2d6-286ce8888f1f.jpg

Answered: Let f be a continuous functio to R. Let…

Math

Advanced Math

Let f be a continuous functio to R. Let a and b be two distinct ntained in U and fbe differentiable 0 (h all

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

See similar textbooks

Related questions

Q: Q-1 min их, тих, х? + ж, =у

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 9.8 m/s² 5 x 105 m/s x 20 × 10³m Please explain how the answer to this is 2.45 x 10^-8 s^-1

A: The answer for the given problem is 9.8•10-10m-1s-1

Q: Find the standard matrix of the linear operator M: R2 R2 that first reflects every vector about the…

Q: 15. (a) Calculate e with an error of less than 10-6. (b) Estimate the error in the approximation…

A: a. Let fx=ex We know that the Maclaurin series is fx=ex=1+x+x22!+... The remainder term is…

Q: Given that the matrix A has the Singular Value Decomposition A = UΣVT, where: 6000 -(1)-(-(110 =…

Q: The sequence of eigenfunctions of a symmetric kernal can be made orthonoramal.

Q: Suppose P is false and that the statement (RS) → (PAQ) is true. Find, without using a truth table,…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If…

Q: Find f(x) + g(x) when f(x) = ex and g(x) = e³x

A: Given functions are f(x) = e4xg(x) = e3x

Q: f P is the projection on a closed linear subspace M of a Hilbert space H, then M is invariant under…

A: Let M be invariant under T . Let x by ant arbitrary vector in H , then Px in M , and so TPx is in…

Q: Explain whether the cylindrical surface and the spherical surface may be homeomorphic?

A: To explain: Whether there is a chance that the spherical and cylindrical surfaces are homomorphic.

Q: Prepare (by hand) the final (simplified) equation system necessary to obtain the least squares…

Q: Find the volume of the solid that lies inside both the cylinder x² + y² = 16 and the sphere x² + y²…

A: Given cylinder and sphere x2+y2=16x2+y2+z2=36 clearly, Here we need to find volume inside both…

Q: Let Y be the portion of the sphere x² + y² + (z − 2)² = 4 which lies below the plane z = 3 with…

A: Given ∫Cz2+3yi→+2z-2xj→+z2k→.dr→ The portion of the sphere x2+y2+z-22=4 and plane z=3

Q: Let P(x, y) = Shop x is open on day y" Let the domain of discourse of x be shops o campus and the…

A: let Px,y:= " shop x is open on day y" let the domain of discourse of x be shops on campus and the…

Q: Browse the internet and find a very nice differential equation model (not among the ones covered in…

A: To find: A differential equation. The procedures below must be taken in order to write a…

Q: Suppose we have a nxn linear system A = 6, but that the coefficient matrix A is not strictly…

Q: Question 4 (a) Calculate the following: i. the area of the region in the first quadrant bounded by…

Q: (c) Let f: [0, +∞) → R be continuously differentiable. Show that there exist continuous, positive…

Q: The average weight of sidens (motor cars. 759) 008++ 7ohe-e79 = (7SM by coff parents 19

A: The average weight is given by Wt=6t2-240t+4800,5≤t≤27 Plot the graph of the given function The…

Q: I am asking ,How to get roots In Scientific calculator. I don't need solution.

Q: . Solve the boundary value 2 at² = 9² au əx² conditions U(x, 0) = 0, U₁(x, 0) = 0, lim 110) f(t).…

Q: 55 The fuel efficiency (in miles per gallon) of a sports utility vehicle weight according to the…

A: # for c part mention the table as in lecture notes Given E(x)=0.0000016x2-0.016x+551800≤x≤5400 Find…

Q: functions such that f→fa.e. on a measurable set E of finite measure, then given n> 0 there is a…

Q: 2. Jack went on a hike for 2 hours and 15 minutes. According to his fitness watch, he burned 1013…

Q: -0.4x2 3.2x2 -2x2 11x3 -0.9x3 2x4 X4 5x4 4x3 10x3 -0.4x4 -6.xs 7x5 4.8x5 6xs 6 = -2 ||||||||| 9 1

A: Given: System of equations -0.4x2+11x3+2x4-6x5=6 3.2x2-0.9x3+x4+7x5=-2 -2x2+4x3+5x4+4.8x5=9…

Q: If the solution is Solve the initial value problem y = co+c₁x + ₂x² + c₂x²³ + C₁Xx²+ + C5x³ + 6x6…

Q: Find the sequence generated by the following exponential generating function: f(x) = e^x − e ^−2x +…

Q: A chemical compound decays over time when exposed tion to the power of 3/2. At the same time, the…

A: The differential equation that shows the rate of decay of the chemical compound is as follows:…

Q: Calculate the geodesic curve of the surface x^2 +y^2 -z=0

A: Given That : z=x2+y2 To Find : geodesic curve

Q: The following is the function for electricity costs in Erin's city of residence. C(k)= = 9.86…

A: Given That function for electricity cost c(k)=9.86+.0945k 0≤k≤60066.56+0.12557k…

Q: Prepare (by hand) the final (simplified) equation system necessary to obtain the least squares…

Q: For a matrix C 8 Arg(a + bi). (8) Select one: O True O False in real canonical form (real normal…

Q: Q5) Test the completely state controllable for the following system: * = [₂²][²²]+] ₁² น 2

Q: Suppose T: P3-M2,2 is a linear transformation whose action is defined by c+d b+d T(ax³ + bx²+cx+d)=…

Q: 3. Define the function f(x) (a) Evaluate lim f(x) x →0+ (b) Evaluate lim f(x) x-1 = 2x n+m m x & Q m…

A: Here we use the way of function definition. And use the definition of limit of function at a point…

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent: The…

A: Let us consider an alternating series ∑n=1∞(-1)nan The series is convergent if, limn→∞an=0 an is…

Q: Without calculation, decide if each of the integrals below are positive, negative, or zero. Let W be…

A: Please check step 2 for solution.!

Q: (a)Define laplace transform of a function f(t) and its inverse. Is inverse unique ? (b) Obtain a…

Q: 4. Find a solution of the Bessel's equation of order zero.

Q: Question 3-) Let z(t) = sin(3πt + 0.3) (a) Find the minimum period for z(t). (b) Find the fourier…

Q: Consider the function - f(x, y) = 2x² − 4x + y² − 2xy subject to the constraints x + y ≥ 1, xy ≤ 3,…

Q: Q) Calculate the coordinates of the center of mass of the disc D bounded by the circle x² + y² = 2y,…

A: Given: The density of the disc is: fx,y=1+yThe disc D is bounded by the circle x2+y2=2y We have to…

Q: C) Apply 4 iterations of the Secant method, taking initial approximations t₁ =16 and ta=26, to…

Q: Consider the ollowing linear system, 2x1 + x₂ − x3 + 2x4 - 4x₁ +5x₂ − 3x3 + 6x4 - -2x1 +5x2 - 2x3 +…

A: Let us consider the system of the equation AX=b. To solve the equation, Find the augmented matrix…

Q: , Evaluate, in spherical coordinates, the triple integral of f(p, 0, b) = cos , over the region 0 ≤…

Q: 1. Find the area of the region bounded by the boundary conditions below: (complete with graph) a. y…

A: We have y=x+5 , y2=x , y=2, y=-1 Now, the region can be graphed as below: The area lies from y=-1…

Q: given in polar coordinates. (i) Create a table r(0) 0 r(0) r(0) -5m/12 76 r = 5 cos² (0/2), (-= < 0…

A: Given a function is polar coordinates rθ=5cos2θ2 where -π≤θ≤π To create a table for different values…

Q: The sequence of eigenfunctions of a symmetric kernal can be made orthonoramal.

A: A symmetric kernel's eigenfunction sequence can be rendered orthonormal. Assume there are m linearly…

Q: Stacey purchased a car for $58,300; she paid 5% of the cost as a down payment and financed the…

Q: Question 3 3 pts Last month, Kaitlin's average daily balance on her credit card was $1,268.52. The…

Question

Let f be a continuous function on an open subset U of a
Banach space X into R. Let a and b be two distinct points in U such that the
segment [a, b] is contained in U and fbe differentiable at all points of [a, b]. Then
f(b)-f(a)=Df(a+0 (b-a)).(b-a),

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here