et {an} and {bn} be sequences such that an < bn for all n, lim an = a, and lim bn = b. Then a > b.

Q: 2. 8 cos + i sin 8 8 10 + i sin 16 cos 16

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Q: The initial value problem y" + 4y" + y' - 6y = -12, y(0) = 1, y'(0) = 4, y"(0) = -2 is given. If the...

A: Properties of Laplace transform L-11s-a=eat L1=1s Ly'''=s3Y(s)-s2y(0)-sy'(0)-y''(0) Ly''=s2Y(s)-sy(...

Q: Find a primitive third root of unity e F7, then verify by direct computation that (5 - 5)? = -3 in F...

A: Primitive roots are those x which satisfy x^k = 1 mod n

Q: 2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 b...

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Q: Let f (2) = zi + (z – 4). Part (a) Integrate the function f (z) along the curve C given by z = t+it?...

A: We will use the basic knowledge of complex analysis and line integrals of complex-valued functions t...

Q: In triangle ABC, c-150 cm, angle C-70°, angle A=45°. Determine the length of the median drawn from t...

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Q: You will find Taylor polynomials for 2 functions, then graph them on Desmos and insert screen shots ...

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Q: + x

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Q: 5 2.51. s(s-2)3

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Q: Considering the following dynamics of the number of customers for a business, which one of the follo...

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Q: Choose the statement that best describes this graph. O a) Same initial value, different rates of cha...

A: We know that the value of the line at x=0 is called the initial value. Since the value of the two li...

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

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Q: I need help :( can you please explain how the graph above can be used to solve the equation and what...

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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: The base of a certain solid is the triangle with vertices at (-6, 3), (3, 3), and the origin. Cross-...

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Q: se the method of variation of parameters to determine a particular solution lo the given equaliol 10...

A: we have given the differential equation y'''-15y"+500y=e10x we have to find the particular solution ...

Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (х — 2)? 3D 4(у+ 2) ...

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Q: How many even factors does the number 3,809,975,400 have?

A: We will use the basic knowledge of number theory and prime factorization to answer this question pro...

Q: Show that if z = x+ iy, then: | cosh-z|2 sinh x Hint: use the equation: | coshzf = sinhx+ cos"y

A: We have , z = x + iy We know that ,  coshz = ez + e-z2 Therefore , cosh (-z) = e-z + e-(-z)2 = ez + ...

Q: dy 3. dx y – x + cos - -

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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: E. Determine the set of points satisfying the condition described by |z – 2i| + |z + 4i| = 10. Then ...

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

A: Solution:-

Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotated ...

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

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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: Try to fit any two moving averages models to the following data and discuss its performance. YEAR 20...

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Q: х* + ах + 2bx + 2ab + 2x3 — ах* + 6bx? dx х4 + аxх3 + 2bx3 + 2abx?

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Q: Question 18 T/2 Evaluate using Wallis' Formula: sin7 x cos5 x dx X CO

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Q: 2. y"+7y'+12y= 0, y (0)= 1, y'(0) = 2

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Q: dy +ky = a sin bx dx %3D Show that the solution of the differential equation is given by: 2 +b²+ab K...

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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: 10 Vx2 + 9 -dp- a. 15 .

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Q: Stephanie is shelving books in a display in TH the school library. She has 3 different books cla wit...

A: Stephanie has 3 different books with 4 copies each. So Total books = 4x3 = 12

Q: 3 Find A= 5 2 B =| 3 4 う AB -2 -2 り BA 2.

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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: 4dx + (x -y + 2)²dy = 0 %3D

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Q: 5. Find the Taylor series for f(x) = centered at a = 4. 1.3.5..... (2n – 1) |1+E(-1)"- (r- 4)" n! 23...

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Q: y-5dy – y-dx = xdx; when x=Y3D0

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Q: Find the general integral of the following first order partial differential equations p+11lq = 7z+co...

A: By Bartleby policy I have to solve only first one as these are all unrelated &amp; lengthy problems....

Q: 03: Use Raabe's test to determine the convergence of

A: We have to check the convergence of the series ∑n=1∞ 1n!nen using the Raabe's test. Let us denote an...

Q: H.W: Evaluate the integral: 11-x 1 || | dydzdx 0 0 x+z

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Q: 2. Give the equation in the form ax + by +c = 0 fo the line & passing through C(-4, 6) with slope 1 ...

A: From the given data we have to find the following value.

Q: etermine if the series converges or diverges n (-1)3п n4 + 1 =1 onsider the power series. Use the pr...

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Q: Suppose a 5-card hand is dealt from a standard deck of 52 cards. How many 5-card hands can be formed...

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Q: dy et-y dx 2.

A: The given problem is to solve the given differential equation using separation of variables method.

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: Σ n=3 nV

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Q: Determine whether the given series is convergent or divergent. Justify your answers.

A: We have given a series ,  ∑n=3∞2n3 We need to determine given series convergent or not. for that tak...

Q: 1 dy 3. С + 2y = sin x when y(r) dx

A:

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.