If both >an and ) b, are divergent then an infinite series of the form n=1 n=1 > (an – bn) is always divergent. n=1

Q: Give a specific symmetric 3x3 matrix whose first row is [1 9 -2] 6. and whose second column is row i...

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Q: (b) Using Laplace transform, evaluate te -2t Cos 2t dt 0.

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Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 2ky + k² = 0 and ...

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Q: Cost Function: The total cost (in hundreds of dollars) of producing x gourmet espresso makers per we...

A: 1) total cost function is given by Cx=6+4x+4 for 0≤x≤30 find C'x then find C'15 differentiate the fu...

Q: Find the x+ iy form of tan(i), arctan(2i), and tanh(i 3º5).

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Q: x²dx Evaluate x2Vx2-4

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Q: Let 0 0 -1 1 0 1 A = %3D | 0 1 (a) Find all eigenvalues with their multiplicities. (b) Find the defe...

A: We can solve this using given information

Q: Consider the differential equation: In(y') • (y') - (y')3 When solving the previous equation, the pa...

A: We are given a nonlinear differential equation and its parametric solution in x(z) , y(z) From that ...

Q: Determine all the roots of z8 - 2z* +1 = 0

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Q: 3 4 S 2. 4 4 2 2 - 4 3 2 A = 4 3 3 4 2 - 4 - 2 2 2 2 3 4 3 + 2 2 3. 2.

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Q: Total personal income of the country (in billions of dollars) for selected years from 195 uotion of ...

A: Given, the Total personal income of the country ( in billions of dollars) for selected years from 19...

Q: ermine the surface area generated when a portion of the curve in the 1st quadrant of = 9(x² – a²) is...

A: We have to find the surface area of region.

Q: Use the definition of differentiability to show that f(x, y) = y² – xy+5x is differentiable everywhe...

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Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (x – 2)² = 4(y + 2) ...

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Q: olve the linear system using Gauss Jordan Method only. 74 6y + 4w - 8z = 315 151 5x +2y - 2w = 105 1...

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Q: Find the area bounded by y = sin2(x) and y = sin³ (x) from sI< %3D

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Q: Use the Putzer algorithm to determine the exponential of the following matrix: 1 1 0 3 -2 0 3 -4 A =

A: The problem is related to linear algebra and matrix. We have to ask exponential of the matrix. First...

Q: Hewin If Z =R Cxxy]:and u=x-yg V=x²-y 그를 + show that

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Q: Consider the system of linear equation below: A+ 2B + 3C + 4D = 8 2A - 2B - C + D = -3 A - 3B + 4C -...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: The orthogonal projection of a vector a→ onto a vector b→ is calculated using the formula: orthb→a→=...

Q: Prove or disprove the following statements: justify your answers. (a) Let A E Mnxn(C) have real entr...

A: We will prove the given statements or give counterexamples to disprove them.

Q: Find the Laplace Transform of the following. 1. F(t) 2. F(t) 3. F(t) 4. F(t) = e-tsinh (4t) 5. F(t) ...

A: To answer the given questions we shall use the following table of Laplace transformations           ...

Q: Consider the series In(k) k2 a) Enter an integral whose convergence or divergence is equivalent to t...

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Q: A local Chocolate Factory produces 3 varieties of Chocolate A, B & C. Ron bought a chocolate of each...

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Q: You have an internship where you are helping track revenue and sales. Suppose that p is the price in...

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Q: Find the Laplace transform of the following functions. a) f(t) = t sin tcos t. b) f(t) = te"8 (t – 2...

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Q: Prove that 1 + p'2 p4 where primes denote differentiation with respect to 's'. 1. x"2 + y"2 + z"2 %D

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Q: Solve the given linear system. 3 1 -1 1 -8 X' = 2t 1 X(t) = %3D

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: Evaluate the moment Mx and My of the region bounded by x + 2y = 6, x = 0 and y = 0.

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Q: х* + ах — 2bх — 2ab — х3 —2ах? -2bx? х4 + ах3 — 2bx3 -2аbx? | dx

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Q: 2. Determine if the series n n4 + 1 n=1 Σ (-1)3n converges or diverges. 3. Consider the power series...

A: Series and sequences

Q: Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at...

A: Given suppose heat is lost from the lateral surface of a thin rod of length L in to a surrounding me...

Q: Evaluate the expression 2 1+i 2 1+i (2i – 1) 1+i 1+i

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Q: (c) The function, y(x) = 2.0 sinx + 3.00 Inx + x is to be evaluate for x = 1.26. The constants and t...

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Q: Find the antiderivative, G(t), of the function g(t) = (2n²t2 - t)V2n2 -t².

A: As per the company rule, we are supposed to solve only one problem from multiple problems. Therefore...

Q: Binomial Distribution: (n = 6, p = .2) Find (Use these data in Prob. 1-3) 1) Pr (r < 2) 2) Pr (r 2 1...

A: We have to find the probability of binomial distribution.

Q: Evaluate the moment M, and M, of the region bounded by y = 2x + 1, x + y = 7 and x = 8.

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Q: Using integration by parts, | - | x sin(x²) dx x* cos(x²) dx = k – Then k is?

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Q: 2. Compute the minimal polynomial of the following matrix (with coefficients in R) WITHOUT comput- i...

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Q: Solve by the cigenvalue-cigenvector method the following differential equations: (0) r2(0) ]-[ 4. %3...

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Q: How many years are required for an investment to double in value if it is appreciating at the rate o...

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Q: Call a function f :N - N eventually nondecreasing if the set decr(f) {n eN|S(n+1) < f(n)} is finite....

A: The problem is related to calculus and the topic is countability. We have to ask about range of the ...

Q: Find the selling price of a dvd set which costs Rs2109 and markup is 30%on cost.what is the amount p...

A: Given: Cost price of the dvd set is Rs 2109 Markup = 30% on cost price.

Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

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Q: solve for the function, x^3- 0.03x^2+2.4x10^-6=0, assuming stopping criterion of es=0.1

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Q: 1. Construct the multiplication table for the the group Us = {1,a, a², a°, aª} where a = 2ni e 5

A: As per our guidelines we are suppose to answer only one ques. Answer of question 1 is as follows:

Q: What Mclaurin Series this function represents: -를- n+1 = x n + 2 3 O a. In(1+x) O b. cosx O c. sinx ...

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Q: 2 2 The matrix A has an eigenvalue A = 8. %3D 3 7 Find an eigenvector for this eigenvalue. Note: You...

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Q: How many years are required for an investment to double in value if it is appreciating at the rate o...

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.