Problem 1. Suppose f: R → R is a continuous function which can be uniformly approximated by polynomials on R. Show that f is itself a polynomial.

Q: Let f(x) = 3x + 2. Use the € – d definition to prove that lim 3x +2 1. x→1 Definition. E-d proof.

A:

Q: Which of the following polar equations represents a cardiod or heart- shaped curve? r = 4 cos 20…

A: Here given polar equations  r= 4 cos 2θ ......(1) r= 3+3 cos θ .......(2), r= 2 cos 2θ .......(3) r=…

Q: 1. Transform the unit square under 0 1 0-1 cos 45 sin 45 -sin 45 cos 45 10 03 Say what each…

A: To find: the transformation of unit matrix under given matrices.

Q: Let (X, T) and (Y, T₁) be two topological spaces and let f be a continuous mapping of X into Y. O If…

A: Solution

Q: (-X, -1 < x < 0 Find the Fourier series expansion of the function f(x) = x, 0 < x < x

A: We have to find the Fourier series expansion of the given function.

Q: 2. Let X be a normed space and UC X a closed subspace. The subspace U = {X E X' | Vu EU: X(u)=0} is…

A: Suppose that there existx∈U⊥⊥:=x∈X : fx=0, for all f∈U⊥ such that x∉U.¯Evidently, x is not zero.…

Q: -{1 f(x) -2<x<0 0<x<2 Ans. Fourer series...

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: 4) USE THE 2 0 2 0 A 1 0 || GAUSS-JORDAN -3 0 -1 2 - 4 1 1 1 -3 -4 REDUCTION METHOD (SINE PROCEDURE)…

A:

Q: By 28(1 + i√3) solve all of its z-values if it is raised to 14.

A: Solution : To find, 28(1+i3)14 =56eiπ3+2nπ0.25 where, n∈ℤ n=0,1,2,3 =2.74eiπ12+nπ2

Q: 8. Given vector v = (4,-5) a) If we want to represent v in the form v= AB where A = (-2, -3), what…

A:

Q: Find of z= In(xy) 8²y

A: For a function of the form: z=f(x, y), the partial derivative with respect to y is calculated by…

Q: 5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1,…

A: Let R be the relation on the set 1 , 2 , 3 , 4 , 5 containing the ordered pairs  1 , 1 , 1 , 2 , 1 ,…

Q: dius 9 units and center dius 3 units and center

A:

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: The volume of a solid S in polar coordinates bounded by the surfaces z1=f1x,y and z2=f2x,y can be…

Q: 5. (D²2D+1)y=e* arctan x

A:

Q: Let f be a continuous function defined on the closed interval [a,b] and differentiable on the open…

A:

Q: Find a. a. b. ow ax dw dz dw dx y and b. (2,-2,-2) (2,-2,-2) ow at the point (x,y,z) = (2, -2,-2) if…

A: To find- Find  ∂w∂xy ∂w∂zy at the point x, y, z = 2π, -2, -2π if w = x2 + y2 + z2 and y sinz + z…

Q: В =8 7=1 20 - (43(БА 0.03 796 A A= Ву+792 = 89хуг Р=В+29 5+22 У =2

A:

Q: Joanna is investigating how a harmful substance from pollution is absorbed by the human body. She…

A: To find the general solution to the given system of the differential equation.…

Q: Simpson's Three-Eighths (Use n = 12) 9. So¹ (3x²+3) dx 10. (2 sin x + 3cos 2x) dx

A: First we find general solutions: 9.  ∫13x2+3dx=∫13(x2+1)dx=13∫1(x2+1)dx=13tan-1x +c    then…

Q: 10. (a) Find two lines that are parallel to the plane (x, y, z) = (1, 0, 2) +t₁ (1, 2, 3) + t₂(4, 5,…

A:

Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x-2y+3=0 and y = 0.…

A: Given that,  R be the region bounded by y=4-x2 and 3x-2y+3=0 and y=0. (a) Divided  the region in two…

Q: Give the area (in square units) of the circle with an equation, * x² + y² = 6x-8y. The area is 625π…

A:

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim X→2…

A:

Q: B CX 1. Establish two perspectivities so that a projectivity is established between A, B, C and A',…

A: Solution:  1.) Using the Desargues theorem, projectivity is established between A, B, C and A', B',…

Q: By considering different paths of approach, show that the function below hile no limit as…

A:

Q: Find the dimension of the splitting field of each of polynomials x+1 and x² - 2.

A:

Q: 4- Evaluate the following integral * sin 0 de -5\32 -5√π\32 O 5√n\32 5\32 KIN 0

A: Use Walli's formula to evaluate this integral as in next step.

Q: The Laplace transform of the function u: [0, ∞) → R [(t-2)² + (t-2) sin(5(t-2)), for t > 2, =…

A:

Q: d. 21 ST 8 3 2

A: Introduction: The gamma function, denoted by, is a typical extension of the factorial function to…

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 5. Lim xsinx x→ 0+ 5

A:

Q: Sketch the graph of the function f(x)= H

A: Given,         f(x)=x2x2-x

Q: Parabolic cylindrical coordinates. Parabolic cylindrical coordinates u, v, w are defined in terms of…

A: As per the question we are given the parabolic cylindrical coordinate system. And we have to find :…

Q: Discreet Mathematics Given F (A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD, express F (A, B,…

A: Given:  F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD To find: Minterm list form

Q: Calculate the integral approximations T4 and M4 for fr5 dx. Your answers must be accurate to 8…

A:

Q: Evaluate the iterated double integral JI-X² ( [√x² sin (x² + y²) dz dy dx

A: A a couple of imperative is a specific imperative of a characteristic of numerous actual variables…

Q: 4. Let R be the relation {(1, 2), (1, 3), (2, 3), (2, 4), (3, 1)), and let S be the relation {(2,…

A: To find the composition of two relations R and S . the domain of S°R will be same as domain of R…

Q: Find May of the volume, if the solid of density & (x,y,z) = Z and the lower parabola is (Z₁ = x² +…

A: Given that  Lower parabola: z1=x2+y2 Upper parabola: z2=4−x2−y2 Density: δx,y,z=z To determine:…

Q: 10. Particular solution of y"-4y' + 8y = x³, when x = 0, y = 2, y' = 4

A: We have to find the particular solution of y''-4y'+8y=x3,  when x=0, y=2, y'=4.

Q: [[F(x, R th limits of integration B D -IT² f(x, y) dA = f(r cos(0), r sin(0)) r dr de (Click on…

A: In this question, the limit of integration of polar coordinates is determined.…

Q: Find the interval of convergence for each power series. Include endpoint convergence tests when…

A: To find the interval of convergence of the given series :-

Q: Exercise Set 1.3 In Exercises 1-2, suppose that A, B, C, D, and E are matrices with the following…

A:

Q: Draw a Venn diagram to represent each relationship. 1. Some people check out books 2. There are no…

A: We have "There are no freshmen in AP Economics" So, we need to have a Venn diagram such that…

Q: 1 Consider the series (-1)-¹ Σ(−1²+ (x+1)* where b is a given non-zero constant. Find the nb2n 1=0…

A: Infinite series: An infinite series is represented by ∑n=0∞ anx-cn, where an is the coefficient of…

Q: Find the total areas of the shaded regia 47. y=x√4_7²

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the…

A:

Q: 1. The Maximum point of y = (x²+2x+10) (x-3)

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Paper sheets are required to make a stack of 8cm height. Each paper is 2.5x10-4. How many are…

A: Solution

Q: The relationship between training costs (x) and productivity () is given by the following formula, y…

A: Given- The relationship between training costs (x) and productivity (y) is given by the following…

Q: Newton-Raphson Method Description of task. 21. This is a method which involves using an iterative…

A: Given function is f(x)=5x2-4x32-6 Then…