1. Evaluate y'+3y²+2y=e-t , y(0)=4, y'(0)=5

Q: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given conditions are met,…

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Q: Let xbe inner Product x+y Lx_y

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Q: f(x) = = x, over the interval - 1)=-4 [002-2008 22 +cos 3.- cos 42+...] f(x) 2 [sin zsin 2 J II sin…

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Q: Determine whether the given differential equation is separable. (xy³ + 2y³) dy-7xdx = 0 Is the…

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Q: 3. Find f'(x) if f(x) = 2x + sin³ x

A: Here we use the quotient rule of derivatives. It says ; d/dx (u/v)=( v*u'-u*v' )/(v^2) Where u and v…

Q: 1. Let f(x) = 5, if x>1 f(x) = 2, if x < 1 f(x) = undefined for x = 1 Find the following one sided…

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Q: Show that the line of intersection of the planes x +y-z = -12 and 2x + 4y - 3z = -8 is perpendicular…

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Q: (xth

A: Here in the given problem, we have to calculate (x+h)3 this can be done by applying direct identity…

Q: 1)Determine whether the Fourier series of the following functions converge uniformly or not.  f(x)…

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Q: 5. Use Cartesian coordinates to evaluate JIJ ² av where D is the tetrahedron in the first octant…

A: As there are multiple questions with subparts, I am doing the first question only as per the…

Q: L{12te-³t} 12 a. (s+3) 12 b. (s+3)² 1 C. (s+3)² 12 d. (s+3)³

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Q: Problem S 1. Show that the first graph below can be constructed for the second graph 2. Verly the…

A: Part (1) The first graph can be constructed using the second graph by introducing a new vertex and…

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

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Q: Suppose that Bob has used two distinct primes p and q to create the public modulus n = pq and public…

A: RSA algorithm: 1. Choose two distinct prime numbers p and q. Take n = pq. 2. Compute λ(n), where λ…

Q: Exercise 25.7.1. Give the Taylor series of the function 1 f(x):= 3x² around the point c = 1 and give…

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Q: Determine the Fourier Series of |f(x) = 2, over the interval 0 < x < 2π and has period 2 ! f(x) = 3π…

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Q: Find the the of 1) Sketch the area ii) Determine the boundaries i) set-up the iv) Integrate 3 x =…

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Q: -1 L-1 [wcose+ssine` s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) 2}, w & 0…

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Q: 1. Use the power series 1 (-1)-1-1, x + 1 n=1 to find a power series, centered at 0, of the…

A: We have to find the power series of given function.

Q: = Solve the following PED: д и ди дı дх² = if u (x, 0) = 2x when 05x52

A: Given PDE is ∂u∂t=∂2u∂x2                    (1) also given that at u(x,0)=2x when 0≤x≤l2 By variable…

Q: 2. Determine all the eigenvalues of the matrix G given below. Hence, obtain an eigenvec- tor…

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Q: Determine the value k with which it is satisfied that the following equation has an infinity of…

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Q: L{tcost + sint} 2s a. (s²+1) 2s b. (s²+1)² 25² C. (s²+1)² 25² d. (s²+1)

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Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: 1 (b) Find Fourier cosine transform of f(x)=< -1 <x< 0<x</

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Q: Find the equation of the line through P = (13, 12) such that the triangle bounded by this line and…

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Q: f(x) = sin nx 14.b The appropriate Fourier series for 100 1-(-1)" a. f(x) = Σn=1 n πT 2 1-12 b. f(x)…

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Q: The solution in implicit form is where C is an arbitrary constant. = C ||

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Q: A graph has 25 edges. The sum of the degrees of all the vertices of this graph is Select one: a. 25.…

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Q: Show that the substitution = e, y = e converts the equation Т Hu ди дzu ди +y2 +x ду? Әх дх2 ду into…

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Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: Determine the Fourier Series of S x, x, 0<x<T |f(x) = { T<x< 2π, and has period 27 ! f(x) = [₁ cos…

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Q: Let A ST and assume that det(A)- 2. Find det(-2A), det(A-1), det((2A)), det(3(AT)-¹), and a det e C…

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Q: A. Determine whether each of the following fictions is (a) continuous (b) differentiable. * (for all…

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Q: For each positive integer n, let Monotone Convergence Theorem. (2n)! Show the sequence +00 converges…

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Q: = -y(2-y). Draw a direction field for the differential equation y' Based on the direction field,…

A: This is a problem of Autonomous DE.

Q: Use the chain rule to find, where First the pieces: dr End result (in terms of just t): 西 | z = x²y…

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Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 6 of…

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Q: 1. Consider finding the root of f(x)=x²-3. Let Estep=0.01, Eabs = 0.01 and start with the interval…

A: Given,        f(x)=x3-3  and with the interval 1, 2.

Q: Suppose T: RR' is a linear transformation 1 1 21 10 3 2 a) Find Null Space Nul(T) b) Find Col Space…

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Q: 3. Find f'(z) and f"(x) if f(x) = ln x + 2 cos³z.

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Q: (3) Prove the Generalized Triangle Inequality: if a₁, a2,..., an ER then la₁ + a2 + ··· + ªn| ≤…

A: We need to prove that if a1,a2,......,an € R  then |a1+a2 +........+an|&lt;=|a1|+|a2|+......+|an|

Q: Is the function a. EVEN h ODD f(x) 1, -π<x<0 1, 0≤x<T

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Q: (x + 3y2)dx - (-6ху

A: Consider r(t)=(x(t),y(t),z(t)), a≤t≤b ∫CP dx+Q dy =∫CP(x(t),y(t),z(t)) d(x(t))dt+Q(x(t),y(t),z(t))…

Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

Q: d interm

A: Introduction: The formula of the law of cosines for a triangle ABC with sides a,b,c is given by,…

Q: 1₁ : [x, y, z]=[7,2,-6] + k[2,1,−3], k = R 1₂:[x, y, z] [3,9,13]+[1,5,5, ],t = R

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Q: 3. Find f'(x) and f"(z) if f(x) = ln x + 2 cos³x.

A: Here we use the properties of derivatives of the function. f"(x)= d/dx (f'(x))

Q: 2. A fertilizer producer finds that it can sell its product at a price of p = 300 -0.1.x dollars per…

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Q: 1. Use Comparison Test to determine the converges or diverges of the series Σ = n=1 (n+1)√√n

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