Use the substitution t= tan to show that secx+ tanx = tan (4+3). %3D

Q: For a group G and a fixed element a ∈ G, define the subset C(a) to be the set of all elements in G t...

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Q: 9. Consider an inhomogeneous differential equation f"(x) = e". a) 'Guess' a solution of the inhomoge...

A: Consider the inhomogeneous differential equation: f'''x=ex

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Q: 8. Let S be a subset of Z defined recursively as follows: • Basis step: 2 e S Recursive step: if k e...

A: Given : base step : 2∈S Recursive step : if k∈S , then : k+5∈Sk-5∈S

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Q: Prove and answer 1 and 2 1. If A is a symmetric matrix, does it follow that the transpose of matrix ...

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Q: 12e* 10) y"-2y'+y =-

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Q: x)-1a) Simplify the diference quotient for the given function. x-a f(x)- f(a)=

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Q: diag(a1,..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main dia...

A: We have to find the Ak.

Q: 7. Let D = acting on infinitely differentiable functions, i.e., for a function f(x) * be the operato...

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Q: Question 1 Determine whether each series converges or diverges. Be sure to name the test used and th...

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Q: Q6. Assume the cost of each basic operation is 2 millisecond. Then, the estimated running time of th...

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Q: Given constants a,b,c, and d such that  x2+ax+12 has factors of (x+4) and (x+b), and x2+cx-4 has fa...

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Q: 1. Find the output needed to maximise profit given that the total cost and demand functions are as f...

A: Find the profit function and then we have to maximize the function using derivatives. 

Q: Writing logical notations to compound statements Let p: Man is rational. q: A century is 100 years. ...

A: The logical symbol "∧" is used to denote "AND". The logical symbol "∨" is used to denote "OR". The t...

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Q: Evaluate SS 5ex+y+" dV over B where B = {(x, y, z) : x² + + z² < 1}. Take = 3.

A: The integrals in the form ∭f(x,y,z)dV is called a triple integral. In this problem, we have to evalu...

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Q: Let V = R?. For (u1, u2), (v1, v2) E V and a €R define vector addition by (u1, u2) H (vı, v2) := (u1...

A: From the given formula of the vector addition, it is obtained that u1, u2⊞v1, v2=u1+v1+3, u2+v2-3. S...

Q: 18. There is a set X for which Ne X and NsX.

A: As N is set of natural numbers , so  for N to be subset of X and N belongs to X , we can consider X ...

Q: Inve e2x Ve2x +1 2. Find dx 2 In e Inv3

A: Given integral is ∫ln3ln8e2xe2x+12 ln(e)dx

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Q: a) Find all m 1 such that 27 = 9 (mod m). [1 0 1] b) If A = |0 1 11 1| is a zero-one matrix, find A ...

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Q: 3. Apply the power series method up to xº to solve the given initial value problem (IVP). Show detai...

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Q: Solve using GAUSS-JORDAN ELIMINATION MATHOD ONLY. x- 2y-3z 0 x+4y +4z = 10 3x +7y +9z=4 -w-2x-4y-6z ...

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Q: 2-Simplify first, then determine the exact value. (sin7n/24 + cos7a/24)2

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Q: Consider relation R={(x,y)|x divides y,xEA,y€A} on the set A={2,3,4,5,10,12,25,30}. (a) Check whethe...

A: We are given a relation : R={(x,y)|x divides y,x∈A,y∈A}  on a set A={2,3,4,5,10,12,25,30}

Q: 3.4. A sequence s,, S2, S3, ... is defined recursively as follows: Sk = 5Sk-1 + (Sk-2)2 for all inte...

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Q: 1 -1 2 1 | -1 1 3 -1 1 Let, A = -1 3 -6 -2 1 4 3 -1 -5 1 a. Find a 5x5 matrix B such that AB = 0, wh...

A: Note :- You can cross check yourself to see that AB = 0.

Q: dz The value of the integral Jc 2+9 where c is the circle z - 3i| = 4 is %3D

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Q: 1 -1 1 -1 1 3 -1 Let, A = -2 1 4 -1 3 3 -1 -5 1 -6, a. Find a 5x5 matrix B such that AB = 0, where 0...

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Q: Convert 1100101, to decimal notation.

A: Given binary number 11001012 we have to convert into decimal notation (base 10)

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A: The parametric equations of a circle centered at origin are x(t) = rcos(kt), and y(t) = rsin(kt).   

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Q: Prove that (- 1)u = - u. [Hint: Show that u + (- 1)u = 0. Use the following axioms and results, wher...

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Q: r - y + z = -4 2x - 3y + 4z = -15 5x + y -2z = %3D 60. 12

A: Introduction: The row operation plays an important role in solving a system of linear equations. The...

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Q: Discretize the differential equation y"+y' +4ty= {t – )), y'(0) = 2, y'(3) = -2 with step-size h =

A: The differential equation given is as follows y''+y'+4ty=δt-32, y'0=2, y'3=-2 The central difference...

Q: Question 7 The following function is homogenous of degree what? f (x, y, z) = x²zy + z² Vx²y² other/...

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Q: Question 1. Let G is a finite group and ø : G → G' be a surjective homomorphism (that is, o is a hom...

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Q: Draw a sketch of a position-time graph, corresponding velocity-time graph, and corresponding acceler...

A: (i) First draw a position-time graph such that vt≠0 at every point.

Q: Given is the matrix а а 2а A = | 1 a 1 a a 1 where a is a parameter. First determine the determinant...

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Q: dz tegra l z2 +9

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Q: Example 12 6-13 Simplify 4+17 Solution

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Q: Theorem (The Triangle Inequality) If A and B are vectors in R", then || A+ B|| < || A|| + || B||.

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Q: (4) a) Solve the initial value problem x'(t) = Ax(t), (i) 4 -5 8. A x(0) -2 1 1 Draw the phase portr...

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Q: 2. Let R be the region inside the curve C :r=1+ cos 0 and to the right of the line l :r = 3 sec 0. 2...

A: To find point of intersection equate both r and find value of  θ which lie in the interval -π,π For ...

Q: Note: Show your work for theses problems. However, you may use a computer for matrix arithmetic. 1. ...

A: Use the slack variables to convert the inequality into an equation.

Q: Suppose that E anx" has radius of convergence R> 0. Let f(x) = E anx". Then n=0 n=0 | f(2) dr = E bn...

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