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Q: Let (an) be a sequence of positive real numbers such that for all n, an+1/an > e^n . Use the Monoton...

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Q: Consider the conservative vector field 4 8 F(x, y, z) = – 3y²cos (3nz),37y sin (3tz) – x2). 2xz, %3D...

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Q: Examples. Justify your answers briefly. (a) Give the Dedekind cut for 5. Your answer should not refe...

A: (a.) We have to find a Dedekind cut for 513 Let A=x∈Q∣x3-5<0 and B=x∈Q∣x3-5>0 1∈A∵13-5=1-5=-4&...

Q: x² – 9 (с) lim х—-3 х + 3

A: To evaluate the given limit. 

Q: Qu:- Prove that funcdiod U = ay - 2x -2 xy-j+x* is hav monic . Firel - funchion v such thut fcas =u+...

A: Solution

Q: Consider the force fields F, (x, y) = (y2 + 2xe",x(3y + xe + 1)) and F2 (x, y) = (M,N). Let C %3D be...

A: Let R be a region in the xy-plane that is bounded by a closed, piecewise smooth curve C, and let  F ...

Q: Lt X and y be metric spaces and T.X- y a Continvous me the image of compact subset M of X under Tis ...

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Q: An experiment consists of rolling a pair of dice once. Let Y be the random variable representing the...

A: For the solution follow the next step.

Q: Consider an annuity with an initial value of R284 129 and monthiy withdrawals of R9 009. The annuity...

A: Given Initial value=R284129 Monthly withdrawals=R9009 Interest rate=5.6%  

Q: Determine the angle between the vectors: x 3i + -3j + -7k and y = 12i + 3j +11k

A: x = 3i -3j -7k  y = 12i +3j +11k  

Q: Determine the values of the variables to satisfy the equation using a) Jacobi and b) Gauss-Seidel. 3...

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Q: hen the image of Compact subset M of X under Tis Compact. lease prove it.

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Q: Q32] evaluate the Cauchy principal value of the given improper integral. dx (x² + 1) (x2 + 9) 1 dx x...

A: These are multiple questions, i.e., the question post has two or more unrelated questions. As per co...

Q: How far does a cyclist travel if she's going 6 m/s in 10 seconds? 1.67 m   0.6 m   60 m   1.6...

A: The speed of cyclist is  6 m/s Time travelled is 10 seconds To find the distance travelled use the f...

Q: er the following statements are true or false. ver will be fined worth a correct answer. al matrix A...

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Q: *+ 4)3 d

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Q: A single row operation was performed on the matrix on the left to produce the matrix on the right. U...

A: The row operations in matrix involves the switching of rows, multiplying a row by a constant and add...

Q: (x? + 4)2 dr Q32] evaluate the Cauchy principal value of the given improper integral. cos X

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Q: A firm faces a demand function of the form P = 90 – 2Q? (a) Plot the graph for their total revenue (...

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Q: (a) Given the vectors u = (0,6, -2, 3) and v = (1, –1, –1, –1), and the point xXo = (-1,1,0, 2) in R...

A: Note:- As per our guidelines, we can answer the first part of this problem as all are different prob...

Q: 6. Explain how the laws of logarithms are related to the exponent laws. Then, explain how these laws...

A: As we know that y=logex⇒ey=x Let us prove one of the exponential law using law of logarithms law To ...

Q: 3c. Show that f (x) is O at least once in the given intervals. f(x) = x sin TX - (x – 2) In x, [1, 2...

A: For the solution follow the next steps.

Q: EP A is a > Find det (2 det (A") A (AT) 2 x? With det (3 A) = 72,

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Q: 1 Vx + 10 — о(х), х — 0 te-2n 10n В. о(1/п), п — о 1 — о(е "), п — sin æ = x- +0(x°), x → 0 3 D. n2 ...

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Q: Show that for a bipartite graph G we always have w(G) = x(G).

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Q: Solve the initial value problem dy – y = 6e' + 72et dt with y(0) = 4.

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Q: g table. f(x) (f• g)(x) x-1 8x 8x + 48 Vx-1

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Q: B. Find the present value of an ordinary annuity with regular quarterly payments worth P1,000 at 3% ...

A: The solution of this question is given below:

Q: 3. Find the general solution to the following ODE: dy dr = 6ry + r*y4

A: Using Substitution, integrating factor

Q: A manufacturing company produces four parts that require the use of a lathe and a drill press. The t...

A: Given- A manufacturing company produces four parts that require the use of a lathe and a drill press...

Q: Show that for any function f : X → Y , there are two functions g : S → T and h : X → S such that (a)...

A: To Show: Show that for any function f : X → Y, there are two functions g: S → T and h: X → S such th...

Q: Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 + ...

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Q: c) Evaluate the integral e* (x + 1) dr, VI – a² using 3-points Gaussian quadrature.

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Q: Which number replaces the question mark? 10 14 6 7 88 12 5 3 ?

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Q: Given Fxy 2) = (z², xy, yz) and C is a triangle in the plane x + y + z = 2 with vertices (1,1,0), (1...

A: We will use basic knowledge of vector calculus.

Q: ng answer will be fined worth a correct answer. If a real matrix A satisfies A" - - A then it is dia...

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Q: 5. Solve the following problems: (a) Choose, refer and use one of the theorems of Vector Calculus to...

A: Solution: Given, F→  = M,N = <-xy-5, -2x-3y2> To calculate,

Q: 3. Set-up (DO NOT EVALUATE and DO NOT SIMPLIFY) the following multiple integrals: (a) /| -a? – 2y? +...

A: Set up Double integral evaluation by bounded region

Q: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

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Q: Let X ~ Exponential(a) where a > 0 is a rate parameter. For a constant 0 > 0, show that the cumulati...

A: We will use basic knowledge of probability theory to answer both the sub-parts given in this questio...

Q: Consider the iterated triple integral in cylindrical coordinates 1 c2+r p3 dzdrde 3r2 (a) Sketch the...

A: Solution,

Q: A vehicle when cumbing up a gradient, consumes petrol at the rate of 1 litre per 8 km while coming d...

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Q: with lim an = 0 and lim f(x) = L,then lim f(an) = L. x0+ Show directly from definition that if an is...

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Q: Q18] A complex valued function is defined as in the following. 22 + (i+1) z + i iz? + (i + 2) z + 2'...

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Q: b) Find the total cost if the marginal cost is MC 3e0.50 and fixed costs are 10.

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Q: Find the complete solution to the following differential equation using MUC: * (D* +2D² +1) y = 3+ c...

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Q: Let G be the solid in the first octant that is bounded by the cone z = 3x2 + 3y2 and the planes z = ...

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Q: 2. Round the following numbers to the nearest one inch: а. 5.76 3D I b. 5.9 = %3D C. 5.5 = d. 6.1 = ...

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Q: A hemisphere of radius R is cut with a plane parallel to the base of the hemisphere, at a height of ...

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Q: 18. In the graph of the function y = f(x) below, A and B are two points on the smooth, continuous cu...

A: Any point on the Cartesian coordinate system is represented as x, y. The gradient (also known as the...