Q2/ Analyze the functions below using the fourier series: ーTくx<0 0, f(x) = {ェーX, TT - X, 0s x< T

Q: Find the inverse of M 1 3] 1 2 2] 2 M : 1 Lo 1

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/6-definition of the derivative to prove that f'(2) = 9.

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Q: x" - x' - 2x = sin3t

A: Consider the given differential equation, x''-x'-2x=sin3t make the auxiliary equation,…

Q: How many subcommittees of 5 people can be formed from a committee consisting of 8 people?

A: The number of ways r items can be chosen from n different items is equal to C(n,r). The formula for…

Q: tet is cosinte toploy on set R show that (R, t) is O NOVmal space- Regualra space

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Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the elements in the alternating groups A3, and A4, respectively.

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Q: z.)

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Q: / Does the following equation satisfied Cauchy-Riemann's equation. (w=z

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Q: Part 3: Solve the non- homogeneous equation y" + 49y = cos(7x) – 7æ² has general solution (remember…

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Q: nduce Such that induced cosinte Sind l Meatric SPaces toplogey. write meatric Spaces Such that…

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Q: (b) By using mathematical induction, show that n(n + 1)(n + 2)(n + 3) 1.2.3+ 2.3.4 + ...+ n(n + 1)(n…

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Q: For the differential equation y' + 8y + 16y = sin(7x)

A: We have to solve the given differential equation.

Q: Give an example of a tiling of the plane that has Regis symmetries but no symmetries of scale.

A: Solution: Rigid symmetry of pattern in the plane: It is motion of the plane that retains the pattern…

Q: Evaluate the integral 1 x3 dx. 1+ x2 0.

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Q: I. Find the probability of the following events. A. A number is drawn from the set {1, 2, 3, ..,…

A: Solution 1) There are twenty numbers in the set. Out of which 10 even numbers and 10 odd numbers.…

Q: 13 in 12 in 9 in CamScanner 5 in

A: To find the surface area of the given triangular prism :-

Q: H.W: Evaluate the integral 3 0 0 1 1. Jaży – 2xy)dydx 2. (x + y + 1)dxdy 0 -2 -1 -1

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Q: I Example 11.17. Find the solution of the initial boundary value problem : 'u u 0 sx S1: subject to…

A: Here we need to solve initial boundary value problem.

Q: |Example 10.27. Find an approximate series solution of the simultaneous equations dx/dt = xy + 2t,…

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Q: For the weighted voting system [12: 8,6,5,3]: a. List all coalitions; identify which are winning…

A: Given weighted voting system [12: 8, 6, 5, 3]. a. To list all coalitions and identify the winning…

Q: a a2 a a 12. Using cofactor method, prove that det N = +99 9 = ab?c'd* - %3D %3D 0 0 c c4 0 d 0 0

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Q: a. Use the long division for solve (x -7x-5x + 2) ÷ (x - 3). b. 30-5х Express as a partial fraction…

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Q: For the following functions Y(s), determine the inverse Laplace transforms. (a) Y(s) =…

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Q: Solve: *+rtand cos 0

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Q: -4 (b) If u find and expressing all derivatives in their simplest 3xy form. Hence, Show that

A: The solution is given as

Q: Given the surface of revolution with equation y? = 3.x. 3 3 Find a generating curve of the surface…

A: Solution :-

Q: A five-member committee is being formed from a group of 9 sophomores and 12 seniors. How many…

A: Given a group of 9 sophomores and 12 seniors. We have to way formed five-member  committees…

Q: Let V = R'and let H be the subset of V of all points on the plane 5r + 2y + 7z = 10. Is Ha subspace…

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Q: Example 10.19. Apply Milne's method, to find a solution of the differential equation y = x - y in…

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Q: HOw many ways can the letters of each word can be arranged? 34. CIRCUIT 8. PARALLEL BLUEBERRY

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Q: Calculate x + y, [Image 19 ) 9. 12 O 15 O Cannot be determined O 13 O 11 O 17 O 16 o o o o oa

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Q: Example 103. Using the sheting metked, solre the boundary value problem : Mosdy=x(x), x@ = 0 and…

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Q: Determine the null input answer of a described system by the equation: y[n] + 4y[n -2] = 2x[n]. The…

A: The solution is given below

Q: Consider p> 2 a prime number, justify that: (P,') = (-1)" (mod p) to any 0 sn sp- 1,n EN. 1.1 1.2…

A: In the given problem we use the definition of combination. Then the problem is solved by…

Q: Question 16 Calculate the sum of x, y, and z in degrees. [Image 16 ] (4z + 6)° 106° 2y O 124 O 99 O…

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Q: Example 10.29. Find the value of y(1.1) and y(1.2) from y" + y"y' = x°; y(1) = 1, y(1) =1, using…

A: Here we need to use the Taylor series to solve the given problem.

Q: 26. In how many ways can: a. five people be seated in a row? D. eight people line up for…

A: No. of ways in which people be seated in a row and Lineup for registration .

Q: Do your calculation in 4 decimal places unless specified in the question. Solve the following linear…

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Q: 7. Find ſxsec¯'xdx using integration by parts made simple or otherwise.

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Q: Express your answer in_rectangular form both in exact value and approximate value. Round off…

A: Using polar form and D'moivers theorem

Q: Find all the roots of f (z) = 2z% + 81/3 – j81 |3D

A: Introduction: A complex number includes the imaginary number i=-1. Due to the presence of this…

Q: I Example 11.7. Solve by relaxation method, the Laplace equation 0, inside the square bounded by the…

A: We need to use relaxation method to solve given problem.

Q: ди I Example 11.9. Solve in 0 <x < 5, t 2 0 given that u(x, 0) = 20, u(0, t) = 0, u(5, t) = 100.…

A: Here, we need to use Crank-Nicholson Method.

Q: O Fvaluate ( 3ds, ahere e is the uppen half of the cincle 13+21 =2 in antibek wise directi on . Ức…

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Q: 5. Rowena would like to invite 7 friends to go on a trip but has room for only 4 of them. In how…

A: Given: Rowena would like to invite 7 friends to go a trip but has room for only 4 of them

Q: Given f(x) = 3 cos x² + 5x – 5. (a) Prove that f(x) = 0 has at least one root in the interval [0, ].…

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Q: 4 Write the equation of the parabola given vertex and a point. a) vertex (-2,5); point (3, 6) b)…

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Q: 4.51. Using the Laplace transform technique, find the unit impulse response of the system described…

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Q: 11) Find the rate of change of output with respect to time, if the production function is Q =…

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