Ifs is(finite or infinite) Contable Set then prove that M*(S) ==

Q: As shown in the required reading or videos the famous Basel Problem, first solve by Euler in 1734,…

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Q: A person who doesn't like to be cold in the summertime has seven (7) pairs of flip flops, four (4)…

A: Let m choices to be made with n1 options for the 1st choice, n2 options for the 2nd choice, … , nm…

Q: (a) For integers a, b, q, r, prove that if a = bq+r then (a, b) = (b, r). (b) Determine (1000, 2025)…

A: Note: since you have  posted multiple questions. As per our guidelines we are supposed to solve only…

Q: You are designing a poster which has a border around the printed portion. The border is 2 inches…

A: Given data:  Design a poster which has a border around the printed portion. Area of poster 300…

Q: The demand curve is P = 30-100p Draw the demand curve and label it The supply curve is P= 20 + 100s…

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Q: *The interval [a, b] for a function x^3 - 4 x- - ...... 9 = 0 is [2,3] O [0, 2] O [0, 1] O [1, 2] O

A: We need to find the interval for a function f(x)=x3-4x-9=0

Q: Using five significant figures in the computations, determine d(sinx)/dx at x = 0.8 from a) the…

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Q: Q2:(a) In Euclidean metric space (R, 1. 1),if A = {y & R: y = []; x E R) then fined the following…

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Q: It costs C(x)=√x dollars to produce x golf balls. What is the marginal production cost to make a…

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Q: Evaluate the integral ₁2-11-1 Sindz.

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Q: Find all the conjugacy classes of D4.

A: We have to find conjugacy Classes of the Dihedral Group, D4

Q: 5. A cylindrical tank is full of water. If the radius and height, respectively, of the tank are 1m…

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Q: 1 Q1) L-1 s(s²-1) 02) The general colution of 11 a) co

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Q: -() 84. State four points where cos x = infinite number of these points? Why is there an

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Q: = √15520124.5793 and Q7: Given that √15500 124.4990, √15510=124.5392, √15530=124.6194, the value of…

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Q: 7. Which word best describes the solution to this system of equations? (x, y, z)=(4,-2,3)+ s(5,-3,2)…

A: Consistent

Q: As shown in the required reading or videos let {an} and {bn} be convergent sequences such that lim…

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Q: .Q11) The general solution of y"-4y' +9y = 0, is: a) y(t) = c₂e²t cos(5 t) + c₂e²t sin (5 t) c)y(t)…

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Q: Given the f(x)=sin(x)+cos(x), find f’(4) at h=0.5 using: (Round off the final answer to 3 decimal…

A: Given that fx=sinx+cosx To find f'4 using step size h=0.5 by the following methods. (1) Forward…

Q: Given the f(x)=xln(x)+sin(x), find the area under the curve from x=2 to x=3 using:​ Riemann Sum.…

A: We can solve this using given information

Q: a) e-3x b) ex ©e. d) Q4) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u'-6u…

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Q: Use Stokes' theorem to evaluate f curlF · ds. F(x, y, z) = y²zi+xzj + x²y²k S is the part of the…

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Q: a) f(x), g(x) and h(x) are c) W (f(x), g(x), h(x)) = 0 d) W (f 02) 6-1 (22) H a)-2coshnt b)-2sinhnt…

A: We will solve question number  9 as you mentioned.

Q: Example 12: Sketch a graph of the function f(x) = x² - 4x³ + 10 using the following steps. (a)…

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Q: (a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert…

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Q: Q2) The general solution of y" + 2y"-y' - 2y = 0, is: a) y(x) = c₁e²x + ₂x + c₂e* c) y(x) = c₁e²x +…

A: Solution :-

Q: 4. y" — 2y' + y = 4e¯t + 2et, where y(0) = −1, y'(0) = 2 2+

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Q: (a) Show that for nonempty HCG, then (H, *) (G, *) a,b Ha*b¹ € H. (b) For some fixed element a € G,…

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Q: ) i) Calculate the simple interest earned on an investment of $ 250,000 after 9 years at a rate of…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: Two spherical tanks are connected as in the figure below. The first tank has the radius 1m and is on…

A: Given, radius of first tank= 1 m radius of second tank= 0.5 m bottom of second tank is 2 m above the…

Q: if y= 3t^2+t+2, x=(2t-3)^3 then dy\dt= 6t+5 false true

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Q: Find the slope of the function F(x) = √√x+1 at the oint (8,3) And find the equation of the tangent…

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Q: Let f(x, y, z) = In(4xy) z² + sin(xy² + ye²). Find fxyz?

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Q: please solve question differential equations 12

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Q: (s+2)2+16 25² +18 (S-2)2+16 2s2+18 Q18) Combine the following power series expressions into a single…

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Q: Question 6 Given integers a, b, c, d = Z, and m, n € N. (a) Suppose that a = b (mod n), and that m |…

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Q: Q4) If the power series method was used to solve the following ODE.. 1 (x-0.5)y". - y' + (x²-1) y =…

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Q: Question 8. (a) In the group Z10, >, find ([2]) and then find the order of the quotient group…

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Q: Find the indefinite integral. (Use c for the constant of integration.) [07- 7i- 8tj + In(t)k) dt.

A: Given the integral                    ∫(7i-8tj+ln(t)k) dt

Q: Using five significant figures in the computations, determine d(sinx)/dx at x = 0.8 from a) the…

A: Given that fx=dydx=sinx To use forward difference approximation to find f'0.8 using step size that…

Q: Show that the closure of a connected space is connected.

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Q: function Q1: For, 0 < |z| < 1, evaluate the following integral where g is analytics g(§) inside and…

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Q: 14. By use of calculator and sketch graphs, find all possible solutions of the trigonometric…

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Q: TASK Double Ferris Wheel Some amusement parks have a double Ferris wheel, which consists of two…

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Q: 3x + 2y + 7z = 4 2x + 3y + z = 5 3x + 4y + z = 7

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Q: Give the Cross products of the unit vectors (i, j, k)

A: This is the problem of vector space and vector calculus.

Q: 1. Find the coordinates of all points on C where the tangent line is horizontal. 2. Set up the…

A: This is the question of the application of Differential Calculus.

Q: Show that any subset of bounded set is bounded

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Q: (d) Determine the right cosets of ((1 2), [1]) € S3 x Z2.

A: I just used the definition  of cosets

Q: Use Euler's method to find approximate values of the solution of the given initial value problem at…

A: Let us start solving the problem step by step using euler method