1. prove every 2nd countable space is Lindelof space. 2. Every Lindelof topological space induced by metric is separable space ****

Q: Solve the following initial value problem using Laplace transformation d?y + 8y = cos 2t with y(0) =…

A:

Q: Consider the inner product space (P2, (,)) with the inner product (p(x), q(x)) = p(0)q(0) + p(1)q(1)…

A:

Q: If p = (u, v, w), show that Ipl < lul + |미 + |wl а. b. Ju| < \pl, ]v] < \pl, ]w] < \pl.

A:

Q: Solve the initial value problem below using the method of Laplace transforms. - 4t y" - 16y = 16t –…

A:

Q: Let M1 F → F be a transformation defined by M1(f) mation? Justify your answer. (1² + 1)ƒ(t). %3D

A:

Q: • Exercise 2 Assuming that i) the sequence of functions {fn(x), x E [0, 2]} converges to f(x) in…

A:

Q: 5 =A

A: Here we use the definition of eigen values to find this-

Q: Use coordinate vectors to test the linear independence of the set of polynomials {1– 212 –t',t+21,…

A:

Q: Problem 6. Find all positive primes p such that n = 1001p satisfies that a" = a mod n for all a.

A:

Q: Define the sequence {b,, } as follows: bo = 4 b, = b,-1 + 2n + 3 for n > 1 Use induction to prove…

A:

Q: r 0 For r E R* let rI Show that H ={rI :r € R*} %3D is a normal subgroup of GL (2, R).

A:

Q: e solution set of the equation 14x5 + 83x4 + 78x3 - 258x2 - 360x + 27= 0 i

A: To find the solution set of the below equation. 14x5+83x4+78x3−258x2−360x+27=0

Q: For an unknown function 9 () and limits a and b (where a < b)if Ja 9 (a) da < 0 then I know for…

A: 8. The function gx represents a curve. That curve either lies above the x-axis or below the x-axis…

Q: For each of the following equations, • find general solutions; • solve the initial value problem…

A: Since you have asked multiple questions, we will solve one question for you. If you want any…

Q: e absolute minimum of f (x, y) = x² + y° – 2 = {(x,y) | y > 0, ² + y? < 4}

A: In this question, the concept of critical point is applied. Critical Point The critical points of a…

Q: solve the linear system [E1=5X-2Y=1 [E2=2X+3Y=8

A: The pair of linear equation can be solve by  1) elimination method  2) substitution method 3) cross…

Q: The binomial coefficient in the extension of (1+x)4 are - a. 14644 b. 14461 c. 14641 d. 16461

A:

Q: Find the Laplace transfomation of the function f(t) : cosh at sinh bt

A:

Q: Solve using Laplace transform technique y"+ 4y = 9t, y(0) = 0, y(0) = 7 %3!

A:

Q: I. Fill the table in. CN Z1 Z2 No. Rec Pol Exp 1. 5- j5 2. 152-34° 3. Z3 25ein 4. Z4 -13-j12 5. Zs…

A: Since you have asked multiple questions, we will solve the Q.8 and Q.9 for you. If you want any…

Q: Consider the inner product space (P2, (, )) with the inner product (p(x), q(x)) = p(0)q(0) +…

A: The inner product on the vector space of real polynomial of degree at most 2 ℙ2 is defined as…

Q: Used cylindrical shell method Find the volume of the solid obtained by rotating about the y-axis in…

A:

Q: 3. Solve the initial value problem by the method of Laplace transforms: y/" + 4y = 2, y(0) = 4,…

A:

Q: y inding a planar drawing. 2. 4.

A:

Q: 2-Solve the following logarithmic equations. a) Log, 2 – log 4 b) 2 + 5(3*) =3(3*) x +7/6=0 -

A: We have to solve the given logarithmic equations to find the value of the variable x. For this, we…

Q: iii) E(-1)"+1 cos²(÷) COS n=1

A:

Q: Question 1 Determine whether each of the following is a power series. For any that are, state where…

A:

Q: Find the volume of the solid whose base is the region in the xy-plane bound parabola y = x² and the…

A: Introduction: Integral calculus aids in the discovery of a function's anti-derivatives. These…

Q: Consider the nonhomogeneous linear system of differential equations: | 16e3t x'(t) = [| 1]×) + [-…

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

Q: (3= +2021) (e금 + e) de +ez-) dz =? 2=4

A:

Q: 3. Using the following table find f(x) as polynomial in x x -1036 7 f(x) | 3 -6 | 39 822 1611

A:

Q: Q2 correct answer

A:

Q: 5. Consider the vector space P2 along with the subspace, H= span {1+ 21°, 2, -f,1-f} Use coordinate…

A:

Q: /hich of these expressions most accurately describes (2a* +2a +3) da?

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Show that the mapping :S3 S3 given by p(x) = xis not a homomorphism.

A: Solution is below.

Q: 1. Prove that an algebraically closed field is infinite.

A: A field F is said to be algebraically closed if each non-constant polynomial in F[x] has a root in…

Q: QUESTION 4 Determine whether A, is a subgroup of S, by using the definition of a normal subgroup. 3.…

A:

Q: Find all the asymptotes of the curve 3x3 2x2y – 7xy? + 2y3 – 14xy+7y² + 4x + 5 = 0 ?

A:

Q: Solve (D² + 4)y = 2 tan x ; x>0 , D= 4?

A:

Q: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its…

A:

Q: Consider the function f(x) = , TE [0, 2]. Construct the Lagrange interpolation polynomial which…

A: Numerical methods: Legranges interpolation of the given data points

Q: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given…

A:

Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

A:

Q: A 6-digit PIN is selected from the digits 0-9. What is the probability that they are all different…

A:

Q: Suppose a classroom has 10 males and 12 females and a committee of 3 is to be formed. Find the…

A: The given question is related with probability. Suppose that a classroom has 10 males and 12 females…

Q: A class is taking a multiple choice exam. There are 8 questions and 5 possible answers for each…

A: Given that, There are 8 questions and the possible answers for each question 5, in which one is…

Q: 10 Find the projection of U = -14 | onto the -15 -4 -4 3 subspace W of R' spanned by -6 | and 6 -1 1…

A:

Q: Use generating functions to solve the following recurrence relations with the corresponding initial…

A: Given the recurrence relation as (1)ak=4ak-1, ∀ k≥1, with initial condition a0=1 Therefore, the…

Q: Solve the following integral equation using Laplace transformation y(t) = 1+ cos(t – u)y(u)du

A: We have to apply the Laplace transform to solve the given problem.

Q: How many values are in the range 17 to 118? 67.5   135   102   100

A: Range = maximum - minimum    Number of values = 118 - 17 = 101