Prove that ℝ with lower limit topology is Hausdorff

Q: 8. Find a fourth degree polynomial function with zeros 4, –2, 3i, and -3i.

A: If x=a is a zero of a function f(x), then f(a)=0 and (x-a) is a factor of f(x).Here, it is given…

Q: Determine whether the function is continuous at the given points. x+30 if x26 6, 0 if x <6 f(x) = Is…

A: Solution

Q: Use the substitution 2 = ry, where z is a function of x, to solve the following differential…

A:

Q: In Exercises 1 and 2, a harmonic oscillator equation for v(t) is given. Using the guess-and-test…

A:

Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

A:

Q: (a) Joseph Flores is paid $452 per week plus a commission of 2% on ali sales. Flores sold $712 worth…

A:

Q: Let the curve C be traced by the vector-valued function Rt) = cos(rt) i + xt j + sin(rt) k. %3D

A: The vector valued functions are usually represented in the form: r→(t)=x(t)i^+y(t)j^+z(t)k^, where…

Q: ulaté the integral: I = (x + 2y) dædy where the region R is defined as: R = {(x, y) E R² :0 <x < 2,…

A:

Q: ct the Fourier series for the function f(x) = (T-x)² for 0 <x < 2n ? %3D

A:

Q: 2. Write the equation for each sequence. 3, 6, 9, 12, 15 b. 5, 7,9, 11 а. с. 3, 6, 11, 18

A: (a)  a1=3=3×1;a2=6=3×2;a3=9=3×3;a4=12=3×4;a5=15=3×5;..an=3×n=3nHence an=3n

Q: Determine the boundlessness and monotonicity of the sequence An 2n+1 Зп -2

A:

Q: 4.1.1. Definition. A separating set or vertex cut of a graph G is a set S C V (G) such that G – S…

A: We have given that ,  The connectivity of graph G , written kG is the minimum size of vertex set  S…

Q: Q4/ Find the centroid of the shaded .area shown in figure below y =4² b.

A:

Q: 11. Find all zeros of the polynomial P(x) = 2x + 7x + 5x³ + 7x?+ 3x. %3D

A: This we shall do by inspection method. The detailed solution typeset in latex is presented as the…

Q: Q4/ Solve the differential equation a) xy. = 1+x + y+ xy dx

A: Solve the differential equation, by Variables separable method

Q: Factor each of the given polynomial equations completely and find all of the solutions. 2x3 – 3x2 –…

A: factor each of the given polynomial and find all the solutions 1) 2x3-3x2-3x+2=0 divide the…

Q: Find the convolution of the two functions: f (t) = 2t and g(t) = (Cos 3 t. %3D

A:

Q: Three sets are defined as follows: M = {natural numbers < < 20} P = {prime numbers < 20} Q = {odd…

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

Q: Solve the following integral: =* dzdy I = R where the region R is: 1. (x, < 2.x, -< xy : Consider…

A:

Q: If n quantities a, b, c, . . . . k are in A.P., then 1 + +....+ is b c 1 - - k 2n 2n (a) a + k (c)…

A:

Q: Raph has gone missing, and his brothers are arguing about who should go and find him. They agree to…

A: For Borda count method For 1st choice = 3 point For 2nd choice = 2 point  For 3rd choice = 1point

Q: In(2n) 2n Determine the convergence of the sequence an If it converges, find lim am Paragraph BIU A…

A:

Q: Describe the graph of the equation. r= (3 – 2) i + 61 j O tis a line in 2-space through the point…

A: Here given equation as r=3-2ti+6t j write it in component form r=3-2t, 6t

Q: lo s²+5s +4 fs) = (క-GS+!ls-6) (s®)

A: To solve given question first we write the partial fraction decomposition of given  question and…

Q: Example 19,9. Show that the equation of the ellipse having foci at z, z, and major axis 2a, is |2…

A: To derive: equation of an ellipse having foci at z1,z2 with major axis 2a. z-z1+z-z2=2a. To find:…

Q: (ii) = 0.3r - 3ry dt = -2y + 0.1zy dt

A: Note: As you asked only Question2 (ii) part so, I answered here only part (ii).

Q: e sets are defined as follows: M = {natural numbers < 20} P = {prime numbers ≤ 20} Q = {odd numbers…

A:

Q: ncess Peach. Which exp

A: Number of teams of two koopalings there = 7C2

Q: Let T: R2 → R4 be defined so that T(-1,1) = (1,0, -2,2) and T(1,2) = (-3,1,1,1). Find bases for…

A:

Q: b) - a +b-c+d = 0 – 2a + b+c-3d = 0 a + 2b - 3c + d = 0 2a + 3b +4c- d 0

A: Let us considre the system of matrix Ax=b Using Cramer's rule, the solution of the system of…

Q: а. b. 4 c. 3 3

A: We know if A1 , A2 ,A3 ,A4 are the angles in quadrant 1 ,2 ,3 ,4 respectively then reference angle:…

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

A:

Q: 2. Consider the system dx = -2x + y dt dy = -2y dt and its corresponding direction field. (a) Sketch…

A: First, knowing direction fields and what they tell us about a differential equation and its solution…

Q: For the cost function below, where C is the cost of producing x units of a product, find the…

A:

Q: y = -4, y= Vx – 4, x= 1 Axis: y =-1 %3D

A:

Q: 4. Solve the following differential equation dy dr TMUTM

A:

Q: That Posseses in finitly Many solutions show that the InregraL equation ges)- f(s) tt S [cos(s+]…

A:

Q: 2 Determine the domain and range of the function y = Vx* + 10x + 24.

A: Domain is the values of x for which this function exist. Range is set of all the values that can…

Q: In figure 8, water flows through a 6.0 cm diameter pipe at 8 cm/s. The pipe then narrows downstream…

A:

Q: Given the series Which ONE of the following statements is TRUE? A. The series converges to 1 by…

A:

Q: 1. Find all equilibrium points for the following system of equations: de = 10z (1- ) - 20ry dt dy…

A:

Q: If money is worth 10%, m=4, find the number of deferred period (d) of a deferred annuity with a…

A: Given , m= 4 Time = 2.5 years.

Q: QUESTION 20 Which of the following correctly evaluates 10P3 ? 10 x 9x8x7 x6x5x4x3x2x1 7x6x5…

A: Permutation

Q: A curve is defined implicitly by the equation ax+ by?=r2 Given that a=20, b32 and r-7, find the…

A: To find  The value of the gradient of the curve where y=2

Q: x +13 25 2.

A:

Q: prove the parallelogramequlity:

A:

Q: Let A and B he two matrices of size 3 x 3 such that det(4) = 2 and det(B) = 3. Then det(38" A") = О…

A:

Q: 48. If a number is selected at random from each of the sets {1,2, 3} and {3, 4, 5}, what is the…

A:

Q: A tank was initially filled with 100 gal of salt solution containing 1 lb of salt per gallon. Fresh…

A: Let the amount of salt in the tank after t minutes will be xt. Since, the initial amount of salt is…

Q: Consider the recursive sequence a =(@+5) with a, =3. If 1<a,<5 then n+1 O A. The sequence (a ] is…

A: