PROBLEM 1. Consider the sequence defined by a_ = n 3n + 3; n 2 1, find the following: 4. 1. Σα i=1 4 2. Σ α i=4 5. 3. Σα i=3

Q: = y(xy³ – 1) %3D dx A + y = ty dy 本ーy= -y e'y? dx

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Q: p(1) 3. Let T : P3 → R³ be defined by T (p(x)) = p(2) p(3) Show that T is a linear transfor- mation,...

A:  First we show that T is a linear transformation. We know that  if U and V are vector spaces over th...

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A: Properties of Laplace transform  L[y'']=s2Y(s)-sy(0)-y'(0) Ly'=sY(s)-y(0) Ltn=n!sn+1

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Q: Y+ 2 - 3W = -2 3x +y -z + 5w - 0 2* + y -2 + ow : o x + y -2 + sw :0

A: To solve the given system of equations using Gauss Jordan method. 

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Q: Evaluate tan(0.942 + 0.429i) C. 0.878 + 0.893i D. 0.707 + 0.636i A. 0.887 + 0.785i B. 0.668 + 0.828i

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Q: 6. y| 11. If D = 0 and x +y = 7, find x. -2 |7 Given D = 1 А. 3 13 В. 4 С. 2 D. 5

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Q: For item numbers 10 A coin is tossed and a fair die is rolled. What is the probability of the follow...

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Q: By using Gauss-Jordan method, the solution of set following above equations will be 2x1 – 4x2 + 6x3 ...

A:  Here A=2-4613-7759,b=524 The argumented matrix is A:b=2-46:513-7:2759:4

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A: We have to find value of x and y by substitution.

Q: Evaluate / = Izl?dz, where C is x(t) = t?, y(t) = , t:2 -1

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Q: 31x = 14(mod127) 26x = 3(mod97)| 3(mod97) 17x = 87(mod101) 24x = 591(mod1001)

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Q: the 'x' with the given below in system of equations: Equation 1: 2wi + 3x(4-3i) = 13 - 66i Equation...

A: Given equations are Equation 1: 2wi + 3x(4-3i) = 13 - 66iEquation 2: 3wi(4+3i) + 25x(1+i)i = -100 + ...

Q: 3. Suppose that r(t) < s(t) on [1, ), and r(t) is continuous and strictly decreasing on [1, 0). If S...

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A: We have to solve the given problem.

Q: Evaluate tanh^2 (4-4i) sech (2+2i). Express your answer in rectangular form in 4 decimal places.

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Q: Solve for x that satisfy the equation x2 + 36 = 9 – 2x2 A. +6i В. +3і С. 9i D. -9i

A: Given expression is x2 + 36 = 9 - 2x2

Q: 4. Let X = C[0, 1] be the space of continuous real valued functions on [0, 1]. Find a subset K of X ...

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

Q: Let E be a set that bounded and c > 0. Prove that sup(cE) = -c inf(-E)

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Q: 2. Construct the truth table for the formula (A→日→ ((B→9>) → A

A: We have to construct a truth table for: (A→B)→[{(B→C)∧¬C)→¬A

Q: |a² + 1 ab ac The value of the determinant A= ba b2 + 1 bc equals cb c2 + 1 са A. a? + b? + c? B. 1 ...

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Q: y" – 2my' + m? memx

A: Given: Determine the general solution of the given, yιι-2myι+m2=memxxmwhere m=4, x=1.

Q: Find the solution and define The interval at which function is değine 2. dx

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Q: Find the Laplace Transform of the following: 2. f(t) = t(vT³ + 1)²

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Q: Consider the power series f(x) =5(-1)* · 2* k +1 Problem 2: (x- 1)3k. k=0 For the duration of this p...

A: Ratio test : Let ∑an be a series of positive reals and limn→∞an+1an=L. If L&lt;1, then the series is...

Q: Simplify 324-4x/2x+18

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Q: (Б) Show that 1 11 %D k(k + 2)(k +4) k=1 4 96*

A: We have to show ∑k=1∞1kk+2k+4 = 1196

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Q: 1) Chris built a rectangular prism Chris used 54 building blocks to make the first layer of the rect...

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Q: Solve 2x < 10. Explain how to find the solution set.

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Q: Q1:Find an orthonormal basis for the Euclidean space Rª that contains the vectors -HH [0] u1 = ; Uz ...

A: Here we have to find an orthonormal basis for the Euclidean space R4 that contains the vector  U1=11...

Q: Use Bisection method to compute the root of the equation f(x) = x² – x – 1 in the interval (1,2) acc...

A: Given equation f(x)=x2-x-1s. We have to find the root in interval (1,2) accurate to within ε=0.2% by...

Q: Q3: Determine the eigenvalues and eigenfunctions for the SLP %3D x*y + 3xy + Xy = 0, y(1) = 0, y(4) ...

A: Given SLP is x2y''+3xy'+λy=0   (1) with condition y(1)=0, y(4)=0 Let x=ez Then (1) will be D1(D1-1)-...

Q: Use an Euler diagram to determine whether the argument is valid or invalid. All snakes are poisonous...

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Q: Find the surface integral F. dS of the vector field F(x, y, 2) = (-æ, -y, yz®) along the part of the...

A: The complete solutions are given below  

Q: Evaluate the value of v-10 x V-7. A. imaginary B. -V70 C. V70 D. undefined

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Q: Evaluate the base (3-4i) logarithm of 10e^2.05i. Express your answer in a rectangular form in 4 deci...

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Q: 9. Evaluate the line integral of F = (2xy + 1,x² + 2yz, y? – 2) over the region C parametrized by R(...

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Q: Use an Euler diagram to determine whether the argument is valid or invalid. No cricket players are w...

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Q: 크) State the negation for each of the following statements. (i) (ii) 12 is a rational number. I am r...

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