Suppose that f: R → R satisfies f(x +y) = f(x) + f(y) for every , y ER. If f is continuous at some point lo E R, prove that there is some constant a E R such that f(ax) : ax for every r E R. f(ax): = ax Please note: is GIVEN TO BE CONTINUOUS AND ADDITIVE. What you have to show is Vx ER

Q: question #4  Part (b.) only

A: Given first order system of equation: dudt=u-1dvdt=v-1 the objective is to sketch the enough vectors...

Q: Use the given graph of the function to find the ætvalues for which Ais not differentiable. Answer (s...

A: A function f is not differentiable at x=a if: i. it is discontinuous at x=a. ii. the graph has a sha...

Q: (d) dln

A: Without loss of generality, we can substitute d and nd in the above expression ∑d|nσ(d) ϕ(nd) = ∑d|n...

Q: Choose the correct steady-state oscillation of y" + cy' + y = r(t) with C>0 and r(t) = sin(4t)

A:

Q: Question 3 > Use the table to find lim f(x) 1 1.9 1.99 2 2.01 2.1 3 f(x) 56.8 6.99 | 6 7.02 7.1| 10

A:

Q: The subject is DISCRETE MATH Give a direct proof of the theorem “The sum of any two odd integers is...

A:

Q: Please solve all the parts

A: First we have to solve given system of equations-

Q: Solve for the unknown. Round decimals to hundredths and percents to the nearest tenth. 3,800 decreas...

A: We have to evaluate 3800 decreased by 18.4%. Note that, the percent 18.4% is already rounded to the ...

Q: Me. Smith wants to put a fence around his yard. The dimensions of the yard are 59 feet by 35 feet. T...

A: Consider the given dimension of the yard as 59 ft × 35 ft. The perimeter of the yard will be obtaine...

Q: Quadrilateral EF GH is a scaled copy of quadrilateral ABCD. Which statement is true. A. Segment EF i...

A: Quadrilateral EFGH is scaled copy of quadrilateral ABCD Therefore, the quadrilaterals are similar, a...

Q: How do I solve this quesy?

A: Hello. Since your question has multiple parts, we will solve the first three subparts for you. If yo...

Q: Which expression has both 8 and n as factors

A: The expression is 8n. Factor is a number or algebraic expression that divides another number or expr...

Q: Solve for the base (in $). Round to hundredths when necessary. What is the base if the portion is $4...

A: Given that the portion is $4,570 and the rate is 55% The objective is to find the base (in $)

Q: x²e* is a solution to y" – 2y' + y = 2eª, and y2 to y" –2y'+y = 2 sin x, then the general solution t...

A: Given, y'' -2y' +y=3ex-sinx

Q: Perform the following calculation below. How many decimal places should there be in your answer? 23....

A: It is given that, 23.12+0.5588+17.9. To add decimal numbers follow the step below. step 1: Line up t...

Q: #12 please

A: Given group table is, * e a b  c d e e         a   b     c b   c d e   c   d   a b d   ...

Q: Please provide well explained, readable for the following;

A:

Q: Problem 5. Let L: R? → R² be given by L(x,y) = (ax+cy, bx+dy) for fixed real numbers a, b,c,d eR. Pr...

A:

Q: Need help with this linear alg. question

A: Concept: Since we have to find  a common point  (X1,Y1) which is lies on both of the line.

Q: linear algebra. can I get help with parts c & d please

A:

Q: A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution contai...

A: Set up a differential equation. Let Q(t) denote the amount of salt in the tank at a time t. The tank...

Q: Taras doggie bakery makes gourmet dog treats. Its most popular flavors are "ultimate peanut butter" ...

A: Given that the bakery makes 2 flavours of dog treats which are "ultimate peanut butter" and "cheesy ...

Q: T 4. Approximate the integral fo x cos xdx with n = 6 using the Composite Simp- son's rule.

A:

Q: Dilate a triangle with the verticies (0,0) (0,2) (2,0) using the scale factor k=3. what is the value...

A:

Q: Please solve all

A: PART A The differential equation is as follows: d2ydt2+2dydt+10y=0.5dxdt+x Now to find the character...

Q: let A= {a, b, c, d} and R= { (a,a), (a, c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. draw a digra...

A:

Q: Give a recursive definition of Binomial coefficient () in terms of (") (we assume n2 k). Do not forg...

A: The objective is to give the recursive definition of Binomial coefficient  n+1k+1 in terms of nkGive...

Q: Finite Mathematics

A: Given,  The US national debt in US in billion of dollars since 1980.  

Q: Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = ...

A: The volume for solid of revolution between the curves y=3x4 and y=0 around the x-axis on interval -1...

Q: 3.5 Consider the Euclidean vector space R' with the dot product. A subspace UCR and æ e R° are given...

A: a) A subspace is given by, U=span0-1202 , 1-31-12 , -34121 , -1-3507 Since basis elements are not or...

Q: Solve for the rate (as a %). Round to the nearest tenth of a percent when necessary. $7.40 is what p...

A:

Q: derive formula for the volume of a Truncated tetrahedron and a Truncated cube Truncated tetrahedron:...

A:   volume of truncated tetrahedron=23122a3 For a regular tetrahedron, volume=212a3 we know that volu...

Q: A person makes an initial deposit of $1000 (and no other deposits/withdrawals) into an account earni...

A: Let the number of full years completed be 'n'. ∴ The amount left after n years is given by          ...

Q: I need help ASAP!!

A: According to the given information it is required to write scientific notation of the given number o...

Q: Please solve the screenshot and explain the steps. The answer is *not* 104.718 as the prior responde...

A: Let's find the triple integral,  ∫∫E∫4x dv, where E is bounded by paraboloid x=5y2+5z2 and the plane...

Q: question 1 only part (b)

A: Given differential equation is, d2ydt2+7dydt+10y=0  

Q: April categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The ...

A: Total amount spent=$2800 % of amount spent on rent =27% % of amount spent on food=20% Therefore Amou...

Q: Solve the following system of equations. 4 2x -. 1 1 3*-y=-12 X = Dlo X

A: Given a system of equations, 2x-15y=45  ⋯⋯⋯⋯113x-12y=-12   ⋯⋯⋯⋯2 Multiplying (1) by 13 and (2) by 2....

Q: Sketch the curve with vector equation r(t) = (t2 – 2, t) in the xy-plane. Indicate with arrows the d...

A:

Q: Find the Fourier series expansion for the following signals once with real coefficients and another ...

A: g(t)=a02+∑k=1∞akcoskw0t+∑k=1∞bksinkw0t from given figure  T=2w0=2πT0=π a0=2T∫02g(t)dt=22∫01tdt=12t20...

Q: Suppose that G is an Abelian group of order 35 and every element of G satisfies the equation x35 = e...

A: