let x be a set and {TiliEI} be a collection of topologies on x. show that the intersection n Ti is a topology on x but the union U Ti ¿EI LEI is not a topology on x.

Q: Many say that baseball, which is commonly called America's National pastime, is a game with a low…

A: 1. The formula for probability is P= Number of successes(outcomes in fever) total number of outcomes…

Q: 4) (y + x² ) dx = xdy Find the general solution to differential equations

A: We have given a differential equation   y + x2 dx =  x dy ydx + x2 dx = x dy x dy - y dx = x2 dx

Q: Exercise 4.27 Let A be a given matrix. Show that the following two state- ments are equivalent. (a)…

A: Given A is the matrix... We must prove (a) and (b).... Let us solve step by step the given two…

Q: 5. Check the convergence of the following series: (2) Σ' (#1) (b) Επ Σ 1998-

A: We need to find convergence and divergence of the given series ,  (a) ∑n=1∞ lnnn+1 Here , we know…

Q: hand written plzz The table shows the number of cars manufactured in thousands by a company for…

A: Solution

Q: ) Evaluate Sxy dx dy R is the region bounded by x =0, x =2, y = x

A:

Q: Three people are coloring the same piece of 8 1/2 by 14 paper. Abby starts on the left side and…

A: The fractions of paper colored by different people are as follows: 12, 34 and 13

Q: Which statement below describes the relationship between the graphs of f(x)= Inx + 2 and g(x) =…

A: Given,      f(x)= ln(x)+2      and     g(x) = 2ln(x)

Q: - Find the solution of the differential equation 2x²5 dy dx = 3xy + y². which satisfy an initial…

A: To find the solution of the below differential equation. 2x2dydx=3xy+y2, y(1)=-2

Q: 1. If C₁ is the segment from (x₁, y₁) to (x2, y2), find Ja x dy - y dx in terms of the four…

A: Using Green 's theorem line integral to double integral

Q: 6x7 matrix with linearly independent (You can choose multiple) Let A be rows, which of the following…

A: Given: 6×7 matrix To find: Solution

Q: What is the solid body surface area formed by rotating the given parametric curve around the y-axis?

A: Given x=costy=sint+t0≤t≤π2

Q: Q11 Find a root of an equation Bellow by using Bisection method Where, & < 0.003, on the interval…

A:

Q: If A is a subset of a metric space X, then show that A = (x: each neighbourhood of x intersects A}

A:

Q: Use the previous problem to show there are infinitely many solutions. to r² = 1+ y² +².

A: As per the question we have to prove that there are infinitely many solutions to the equation : x2 =…

Q: dªx 4. Given the second-order equation of = 6y within the close interval 0 ≤ y ≤ 1. a. Determine the…

A: This is a problem of the application of calculus.

Q: Solve the initial value problem. Indicate the method used. L 4 y² + 4xy = @= 2²³² 1. e-2x² 2 y (0) =…

A: The solution is given as

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: QUESTION 13 What do you call proofs that are based on logical reasoning which starts with a general…

A: (13) Deductive

Q: ग Use the Midpoint Rule to evaluate the integral fx sin(x)dx. D]2 co | Fo 프2 NN

A:

Q: A function f(t) has Fourier transform, F(w) we. What are the Fourier transforms of: (a) f(t-3) (b)…

A: If F(ω) is the Fourier transform of f(t), then using the property of shifting, it can be written…

Q: signing boxes for several products. Each box is a rectangular prism.  The company makes a single…

A: Given that a food company is designing boxes for several products. Each box is a rectangular prism.…

Q: The measure of angle QCS is x^0 Explain why each is either true of false in complete sentences…

A:

Q: root using newton rap

A:

Q: Q4: Discuss the Continuity of following Also find at x = 1 range. and x = 0. Sxx+1 3x+5 -2 -2x+1…

A: a Given function is fx=x+1,    −2≤x&lt;−1x,            −1≤x&lt;03x+5,      0≤x≤2 We have to check…

Q: Q1: A. Find the general solution of the following Initial Value Problem (IVP): y +9y-10y = -40t² -…

A:

Q: Find the flux of F¯ = (x − y)i + xj across the circle x^2+y^2=4 in xy plane

A: As per the question we are given the vector field : F = (x-y)i + xj And a circle in xy-plane : x2 +…

Q: 4) (y+*2)dx =xdy

A:

Q: Content attribution MAY 28 Question Find the lower sum for f(x) = 6 - on the interval [0, 3] using 3…

A:

Q: Q1: A. Find the general solution of the following Initial Value Problem (IVP): y+9y-10y=-40t²-72t +8

A:

Q: 1. Let f(x+iy) = u(x, y) + iv(x, y), where u : R² → R and v : R² → R are defined by u(x, y) = x +…

A:

Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

A: Given: D+x2xD+2y To find: Solution

Q: Exercise 4.27 Let A be a given matrix. Show that the following two state- ments are equivalent. (a)…

A: (a) Let us consider that A=Eijm×n for x≥0. then, Ax=Eijm×nx=Eij×xm×n≥0 it means, Eijm×n≥0A≥0 Now…

Q: SOLVE THE FOLLOWING NON-HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. 1. y" +3y=-48x²e³x

A:

Q: is any linear map, then the foll Im f¹ = (Ker (f))º Ker (f¹) = (Im f)⁰ T0

A:

Q: Convert the ! √ √4-1² 2 0 following to rectangular 32 r³z² sino cos o dz dv do dz dx dy

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

Q: Q1: A. Find the general solution of the following Initial Value Problem (IVP): y +9y-10y = -40t²-72t…

A:

Q: 1. Determine whether u and v are orthogonal vectors. 1. u (6,1, 4), v = (2, 0, -3) 2. u= (0, 0, -1),…

A:

Q: The coefficient of kurtosis of a normal distribution is equal to 3. 3.

A:

Q: 400 X1 600 X3 x2 X4 300 100 X5 (a) Solve this system for x₁, i = 1, 2, ..., 5. (If the system has an…

A:

Q: (b) An edge of a connected graph is called a bridge, if removing this edge makes the graph…

A:

Q: Q2- Reverse the order of the integration ff dy dx + f2f²dy dx equal:

A:

Q: 1. Let f(x+iy) = u(x, y) + iv(x, y), where u : R² → R and v : R² → R are defined by u(x, y) = x +…

A:

Q: interpolation methods are * Olinear interpolation O polynomial interpolation Opiece wise constant…

A:

Q: 10) lim X+ 2x² +1 4X+2

A: Solution

Q: Identify the error(s) in that argument that supposedly shows that if VP(x) Q(a) and 3aQ(a) is true…

A: We have to find the error.

Q: Find the solution of the second order homogeneous recurrence relation:- -3a = 0, n ≥ 2 With a = 1 &…

A: We have given a second order homogenous recurrence relation ,  an + 2an-1 - 3an-2 = 0    ,  n ≥ 2…

Q: I want to buy clothes and resell them for profit. It costs $10 to buy one jacket and $6 for one…

A:

Q: A. Determine if p =-i-3k and q = 61-3j-4k are parallel, orthogonal or neither. B. Find the general…

A:

Q: Let E be a Euclidean space with inner ratic form. For all u, v E E, we have the C y(u, v)² ≤…

A: