By principal of mathematical induction prove that finite product of countable sets is countable

Q: Let f(x) = x² and g(x) = xf(x). Find c = (0,1) as guaranteed by the Cauchy Mean Value Theorem.

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Q: Suppose h(x) = x² - 4x³. Which one of the following is true? Select one alternative: ○ The first…

A: If the derivative of the function is positive in a interval then the function is increasing And If…

Q: Using Euler's method, find the approximate values of the given initial value problem y = 5-2√y, y(0)…

A: Given: y'=5-2y To find: Solution

Q: AL A.A 2) 12/ 12 25

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Q: Q3 Matlab A) Solve the following linear equations (i.e., determine w,x,y,z values) 4w + y +3z -z =…

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Q: Let A be a square invertible matrix. Which of the following is not true? Select one alternative: O A…

A: Since given A is invertible matrix, so det(A) is not equal to zero. It is always true. we also know…

Q: If f has a simple pole at zo and g is analytic at zo, show that Res (fg, z = 20) = g(zo) Res (f, z =…

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. y…

A: We solve the DE  ydx=2(x+y)dy ........(1)

Q: d be distinct nc c+d. Then a 1 b d 1 is

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: In this problem, x = C₁ cos(t) + C₂ sin(t) is a two-parameter family of solutions of the…

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Q: Consider the autonomous differential equation dy/dx = f(y), where the graph of fis given. Use the…

A: For an autonomous system of the form: dydx=f(y), it can be written that: The region above or below…

Q: A) Find volume of body from above Z=1-y² and below Z = x² using Triple integration. B)Solve the…

A: The given problem is to find the volume of the region bounded by given planes by using triple…

Q: Find the general solution of the given differential equation.. dy + +2y=x³ -* dx y(x) = Give the…

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Q: Determine the stepsize that can be used in the tabu- lation of f (x) = sin x in the interval [0,…

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Q: The solution of the differential equation by variable separable method dy (1+y²) (3z²+6) dz 1³ +62…

A: Given :  The differential equation is ;   dydx = 6 1+y23x2+6x3+6x To find : The solution of the…

Q: Find the greatest common factor and the least common multiple of A and B. Write your ans product of…

A: A=33.53.72.113.13B=2.33.133

Q: Determine all the relative minimum and maximum values, and saddle points any) of the function T…

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Q: A tank contains 350 liters of fluid in which 20 grams of salt is dissolved. Pure water is then…

A: It is given that a tank contains 350 liters of fluid which contains 20 grams of dissolved salt. Then…

Q: Let T be a compact operator on a Hilbert space H and (n) be a sequence o complex numbers. Suppose…

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Q: Find the general solution of the given differential equation. 2 +6y= 3 dy dx y(x) = Give the largest…

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Q: Find the area and the circumference of a circle with diameter 6m. Use the value 3.14 for π, and do…

A: We have to find the area and circumference of a circle. Area = phi (radious)^2 Circumference…

Q: Find the general solution of the given differential equation. Xxx + 5y = x³ -x y(x) = Give the…

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Q: B)Z = 1+ Ini, find 121.

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Q: A tank contains 90 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped…

A: Given that a tank contains 90 liters of fluid which has 40 grams of salt. If pure water is added to…

Q: Q1- Choose or branch ( A-find the optimum values of X₁, X2, and X3 3X1 +2X2-X₁ = 1 2X1-2X2-4X3=2…

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Q: Q4) find the soluation of differention equation using exact equation 2) 2xy' = 10 x³y² + y

A: Given differential equation is 2xy'=10x3y5+y The above differential equation is solved as shown…

Q: f(x)=sin(x) is of order 1.

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Q: 2/Solve the following sequence X(n)= n. "u(-n) by using the differentiation property of the…

A: As per the question we are given the following sequence : X(n) = n (1/9)-n u(-n) And we have to find…

Q: 2- If a and b are constant then Variance (ax +b) is equal to a- a² var.(x) b-a² var.(x) +b² c- a²…

A: (2) We know, V(x+b) = V(x)     [ for some constant b ] and V(ax) =a2V(x)  [ for some constant a ]

Q: 2) Sketch the graph of the floor function f(x) = x+31 over the interval [-4,2].

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Suppose A is a 3 by 3 matrix, that {A·A)}* {Q} the eigenvalue √2, and that How many of the following…

A: The given problem is related with linear algebra. Given that A is a 3 by 3 matrix, that 101 , -101…

Q: Use your multiple strips to write 6 fractions equivalent to 1. 2. 3. 4. 5. 6. 25

A: Explanation of the answer is as follows

Q: Which of the following is the reduced row Echelon form of: k 11² ? Select one alternative: 0 k [1 1…

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Q: Please evaluate the determinant using Chio's method.

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Q: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then…

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Q: Consider the function f(x) = 2/x. Calculate the second derivitave at x = 2 numerically using central…

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Q: State the order of the given ordinary differential equation. (sin e)y" - (cose)y' = 7 Determine…

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Q: Solved + 2xy = 3 by using Euler's method to find dx approximate solution up to X-2.9 when h = 0.5…

A: Given y'+2xy=3. Also given that y(1.9)=10, h=0.5 . We find y(2.9) by Euler's method.

Q: Suppose that K is a commutative ring with identity. If and I are ideals of R for which R/I≈ R/J as…

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Q: B)Z = 1+ Ini, find |21.

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Q: Describe geometrically the effect of the transformation T Let A = -(1) Define a transformation T by…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Evaluate the determinant using laplace expansion.

A: We evaluate the given determinant using laplace expansion:

Q: Find the general solution of the given differential equation. 2 +6y= 3 dy dx y(x) = Give the largest…

A: To find the general solution of the differential equation.

Q: 5. Given the equation xy = Arctan(ye*) where z is a function of a and y, Əz əz find and ar ду

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Q: Use SPSS for this Application Exercise A staff counselor predicts that a 6-day training course…

A: Given: No course Course 14.8 11.2 16.3 12.5 14.3 10.6 17.4 12.7 11.2 8.3 16.5 15.6…

Q: Q3 using Euler method, find an approximate value of y corresponding to xe [0 - 0.7], dy Given = x(x…

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Q: 2y (1) (x²+2x) dx = (3 - In x²) dy separable ✔exact linear in x linear in y homogeneous Bernoulli in…

A: As per the policy we are solving first question. Please repost the question and specify which…

Q: A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved.…

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