Question The inverse Laplace transform L is equal to elf. -3s +36 s²+36 Select one: O True O False Give your reasons -3s +36 s²+36 }= -3sin(6t) +6cos(6t).

Q: Write the function f(z) in the form u + iv: (a) z + iz²; (b) 1/z; C - C = . (c) z/z.

A: According to guideline we need to solve only one question.

Q: Prove or disprove. Let A, B and C be sets. If AxC=Bx C, then A B

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Q: Question 9 Find the potential function f for the field F. Here you can assume that the vector field…

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Q: Graph the following function using transformation techniques: f( x)=-3(x+2)^ Description, order of…

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Q: 13. Let : M₂ (R) → R defined by ( oll c C d)) = c = a + d. Recall that the operation on M₂ (R) is…

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Q: rove that let p be a prime and f(x) = ao + a₁ + a₂x² + ... e such that an #0 (p), then the…

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Q: 10. f(x)=4log₁/3(x+2)

A: The given problem is to sketch the graph of the given function and find the domain and range of the…

Q: Find the potential function f for the field F. Here you can assume that the vector field is…

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Q: 43 If y³ - y = 2x, then prove that 2 Hence, show that x² - 1\d²y 27 dx 2 +x d²y 2 dx² dy 1 = -y. dx…

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Q: a. Find all the intersection points of the following curves. b. Find the area of the entire region…

A: The given problem is to find the intersection points between the given polar curves and also to find…

Q: f(101) f'(101) 100 49 If f(x)= II (x− n)n(¹101-n), then find n=1

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Q: 2k+1 2. ΣK=12k²(K+1)² 3. Σ=1 tan-1(k + 1) – tan^1(k)

A: Using limit comparison test:

Q: Question 11 Calculate the flux of the field F across the closed plane curve C. F = xi + yj; the…

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Q: is equal to Select one: True False L-¹ { = + 3 s² +9 52 - 1 1 -/- 1 + 36 ²1 1 3 { } s² +9

A: Properties of Laplace transformation

Q: If a, b, c are positive real numbers. Then prove that (a + 1)(b + 1) (c + 1)² >77 abct.

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Q: DETAILS TDOORS. (a) If f(x) MY NOTES find the Taylor polynomial centered at a=0. Write at least 4…

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Q: If the sequence a1, A2, A3, an is an A.P., then prove that ... ... 2 a²-a² + a²-a²+...+ a²n-1-a²n =…

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Q: Let S¹ = {z E C | |z| = 1}, and let p: RS¹ be the standard covering map given by p(t) = e2rit.…

A: Given that S1=z∈ℂ| z=1. Let p:ℝ→S1 be standard covering map given by pt=e2πit. Now consider the…

Q: $4500 due three months ago but not paid and $2500 due in three months are to be replaced by a…

A: Solution

Q: Determine the eigenvalues and the associated eigenspaces of the following symmetric matrices over R.…

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Q: Solve the given initial-value problem using the Laplace transform: -{- = x(0) = 5. x' + 3x if 0<t<4…

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Q: Question 15 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a…

A: Diagonalization and diagonal matrix D

Q: 1Q: Using Newton Divided difference formula obtain the value of x when y=200 using the following…

A: The given problem is to find the value of x when y=200 for the given table data by using the Newton…

Q: solve: y" - Hý + 4y = 4szt; y(0)=2₁ y(a)=5 using Laplace transform

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Q: Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D…

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Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: 2. Find the rate of interest i such that a 20-year annuity with payments at the end of each year has…

A: The rate of interest is assumed to be i. The accumulated value for a 20-year annuity with payments…

Q: For the matrix A = form. Bottom row is 3 10 i believe 11 -4 -5 21 -8 -11 find a Jordan canonical…

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Q: (c) u-8v-2w=1 u+v+5w = 4 3u-v+w=-2

A: u-8v-2w=1u+v+5w=43u-v+w=-2

Q: Problem 1. 92x² + (a) If A is diagonalizable, that is A = ODO¹. Assume a polynomial f(x) = ao + ₁x +…

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Q: What is the time domain representation of F (s) = (s + 10) (s²-5-2)-¹?

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Q: 17. For the following questions, find a projection matrix P that projects b onto the column sp- of…

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Q: 2 - i)₁ dz, 4 dz, r = {2: 2-1 - i| =

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Q: Consider the planar linear system X' = AX, where -3] A = 3 -2 (a) Find the general solution. (b)…

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Q: 3. Recall that a composition of a positive integer n is a way of writing n as a sum of positive…

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Q: Given the function graphed below, find the following: -4 -3 -2 -1 16 5 3 24 423 -2 -3 -4 12

A: DOMAIN -: THE SET OF VALUES OF x WHERE FUNCTION IS DEFINED. RANGE-: THE SET OF VALUES OF f(x)=y WE…

Q: Let f be a function from A to B, and X, Y CB. Show that f¹(XnY) = f'(X) nf ¹(Y).

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Q: Question 15 Find the work done by F over the curve in the direction of increasing t. F = Zi + -j +…

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Q: 08(3-j2) 7245

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Q: Let f: R\{3} → R\{5} be defined by f(x) = 5x/(x-3). Show that f is bijective and find f-¹.

A: Given f:ℝ\{3}→ ℝ\{5} defined by f(x)=5xx-3. We have to show that function is bijective, and we have…

Q: 44 If x = a[cost +-log tan² t dy T and y = a sint, then find at t= - dx 4

A: x=acost+12logtan2ty=asintt=π4

Q: -x' + y + z = x-y' + z = x+y-z' = (x(0) = y(0) = z((

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Q: 45 If y=1+ 2 a3x² a ₁ (x-a₁) a₁) (x − a₂) (x −a3) [.. X X a2x (x-a₁) (x − a₂) +... to (n+1) terms, s…

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Q: Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z…

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Q: If each of a, b and c is positive and a + b + c = 6, then show that 75 (a + b )² + (6 + ¹)² + ( +…

A: We have to solve given Questions.

Q: -> -->> u, v and w are three non-coplanar unit vectors and a, ß and y are the angles between u and…

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Q: The augmented matrix is given for a system of equations. If the system is consistent, find the…

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Q: Let T = (tij) be the 7 × 7 matrix with (i, j)-entry tij given by 1,1 ≤ i ≤6, tij 0 for all other i,…

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Q: Let S be the portion of the cylinder x2 - 6x +z = 0, oriented by upward-slanting normal vectors,…

A: The given vector field is F = xy, 3xz2,yz.Our aim is to find the flux or surface integral of the…

Q: Solve ty' - y = t²e-t assuming t > 0.

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