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Q: Evaluate the following real integrals by residue theorem 3 03 S <-1 X Sin mx X4 +1 OSH dx πT -m/√z…

A: As per the question we are given an improper integral from -∞ to +∞ and we have to evaluate it by…

Q: 1) э бирорце f a ad да ore integralbl on [a,b]. Show that of -g is also integralible салоз.

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Q: Let fn(x) = nxe-n, for x = [0, 1]. (a) Show that for each x € [0, 1] we have fn(x) converges to 0.…

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Q: Show that (ℤ,∗)?ℎ??? r ∗s = (r +s)−(r ∙ s)??? ??? r,s ∈ ℤ is group using variable r, s and t.

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Q: 8- -cost + 1 y=-sint+t 0 ≤ t ≤ ile verilen parametrik eğrisinin y ekseni etrafında döndürülmesiyle…

A: Given parametric curve as x=-cost+1y=-sint+t

Q: Find the solution of the given initial value problem. 5y""+120y' 800y = 0; y(0) = 11, y'(0) = 26,…

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Q: Day 2 MATH INVESTIGATION Investigate the trend of the graph of equation write your answer in your…

A: Solution: If the line passes through x-axis and y-axis, then we say x-intercept and y-intercept…

Q: (e) For any n €N\{0}, D-C Στις r=1 VI 1 - η 2 11

A: As per the guideline I am answering only first question as they are different questions. We have to…

Q: ) Find the general solution in terms of real functions. From the roots of the characteristic…

A: Given below clear explanation

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find the general solution of the given second-order differential equation. y" + 6y' +9y = 0 y(x) =

A: To find the general solution of the given second order differential equation, let y(x) = Aemx be a…

Q: 6. Evaluate the following real integrals by residue theorem 3 • I= 88 1527 dx (x²+1)(x² +9) ans 12

A: 6. To Evaluate: I=∫-∞∞dxx2+1x2+9

Q: Solve the following: (Show all details) III. Find the determinants of the following matrices using…

A: 1. Consider matrix A=90-7-32-1241 Now,  R3↔R1Factor=-1 A=241-32-190-7

Q: Find the general solution of the following differential equation. y" + 15y' + 56y = 0 NOTE: Use c₁…

A: The given differential equation is: y'' + 15y' + 56y = 0      ......(1) Let y = Aemt (A ≠0) be the…

Q: The table below gives the result of an observation, is the observed temperature in degrees…

A: We have to find the solution of the given problem.

Q: Find the general solution of the system of equations x': ( 2 0 Eigenvalues=₁^₂=2, ^3=2 Eigenvectors…

A: given system of differential equation x'=11121-10-11x which is of the form x'=Ax where A=11121-10-11…

Q: Q₁/Construct the diff. table from •uct the diff. table from the following difa.. X 5 10 15 20 25 y…

A: Given the data x 5 10 15 20 25 y 53 97 144 239 521

Q: Given surface A: 4x² - 9y² = 9(z² + 4) 1. Find an equation of the trace of A on each of the…

A: As per the question we are given a 3d surface A : 4x2 - 9y2 = 9(z2 + 4) And we have to find : The…

Q: MA [ ;] and [ ; ; ] B 37 a Calculate AB by hand and verify your answer using a CAS/calculator. b…

A: As per Bartleby rules we have answer only first 3 sub parts.

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" - y'= et cos(t),…

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Q: Given the following graph of linear function (L₁), y a) b) 10 Write the linear equation for L₁ in…

A: (a) Equation of line L1 is y=-x-2 (b) Equation of line L1 is y=x+8

Q: a) find the domain and range of the function в Сху) =5 4-x2_ye 4-х

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Q: 5. Show that the following functions ry (x² - y²) x² + y² (a) f(x, y) = 0, (b) f(x, y) = if (x² +…

A: We have to show that the following functions have first order derivatives at (0, 0) : (a) f(x, y) =…

Q: Explain why the function f(x) = 2 ln x − x attains an absolute maximum and absolute minimum on [1,…

A: Here first we have to find the critical points of the function on given interval by solving f'(x)=0…

Q: Consider the differential equation = 2xy². Let f(x) be the particular solution with ƒ (1) = 2. a)…

A: As per the question we are given a first order differential equation : dy/dx = 2xy2 And y = f(x) is…

Q: Step 5 We have found the following derivatives of the functions u₁(x) and u₂(x). U₁ = Find the…

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Q: 6. Evaluate the following real integrals by residue theorem 3 & •S= Sin H соз mx ~ (x²+a ²) (x²+ b²)…

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Q: What is the amplitude of the function f(t) = -3cos(πt)? O-3 02 3 О п

A: Amplitude of the function

Q: Find the limit infimum and supremum of Write the solution. Ха = cos ( ^_ 2

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Q: Q4( Let u> 1. Show that 6-6 u-1 >6 ln 6. Justify your answer. Hint: Apply the Mean Value Theorem to…

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Q: Find f(t). f(t) = 0 1 2 3 4 6 (t-3) (t + 3) (t - 3)² (t + 3)² (t-3)³ (t + 3)³ (t (t + 3)²/2 - 3)²/2…

A: Inverse Laplace transform

Q: Solve the initial value problem y = 11cost + sint y = ell cost + 11e-1¹t sint e-11t sint y =…

A: Let y = Aemt be a trial solution of  y" + 22y + 122y = 0. Then the auxiliary equation becomes m2 +…

Q: 8. The order of differentiation in multiple integration of continuous integrand A. has six…

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Consider the differential equation x²y" - 7xy + 15y = 0; x³, x³, (0, 0). Verify that the given…

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Q: 7. Given 8 = 56.78°, u = (-3, 2, -1), v = (2, 3, 4) and ||w|| = √17, find ||lu|| a) b) u. W

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Q: 1. Find the area of the region enclosed by the following curves: x₁ = y²2, and x2 = y. Follow the…

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Q: Use Stokes's Theorem to evaluate integral C of F · dr.  In this case, C is oriented…

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Q: Consider the following. C: counterclockwise around the circle  x2 + y2 = 49  from  (7, 0) to (−7, 0)…

A: Given,   C: Counterclockwise around the circle            x2+y2=49       from (-7, 0), and (7, 0).…

Q: Use Green's Theorem to evaluate the line integral below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0…

A: Given integral is ∫Cx2-y2dx+7xy dy where C: r=1+cosθ,  0≤θ≤2π To Use: Green's Theorem to evaluate…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" - 6y' +9y=t, y(0) = 0,…

A: We have to Use the Laplace transform to solve the given initial-value problem. y" - 6y' + 9y = t, y…

Q: Consider the differential equation x2y" - 4xy' +6y=0; x²,x², (0, on). Verify that the given…

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Q: The sound of a ship's siren approaching the dock has an intensity of 110 decibels. How loud is the…

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Q: Use inductive reasoning to predict the next letter in the following list: O, T, T, F, F, S, S, E,

A: By observing the given list of letters O,T,T,F,F,S,S,E,  we see that: Every letter is the beginning…

Q: Use spherical coordinates to find the mass of the sphere x² + y² + z² = a² with the given density.…

A: We have to using spherical coordinates to find the mass of the sphere x2 + y2 + z2 = a2 with the…

Q: . Find the solution of the given differential equation using the method of undetermined…

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Q: 2. Graph the following exponential functions then state the domain and range [Hint: find parent…

A: Given: 2) y=-32x-2+2 To sketch: The graph of given function.

Q: N Find the limit infimum and cupremum of solution. Xn = n (1 + (-1)^) + n=¹ ((-1)^-1), write the…

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Q: 4. Compute the first fundamental form.

A: Given xu,v=u2-cosv,u+sint, cosv

Q: Determine the values of h(n) for linear phase low-pass FIR filter with 9 taps and a cut-off…

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Q: Local minima are none Saddle points are none

A: Given the function: fx,y=x4+y4+81xy To find the local minima and saddle points of the given…