f(x)= 0, x < -1 2, 11

Q: Draw the phase portraits of the following linear systems and justify the choice of the direction of…

A: As per our guidelines we are supposed to solve only one problem. For the solution of the first…

Q: QUESTION 3 Three years ago, Pete took out a loan of $55,000. The loan was taken out for 10 years…

A: Three years ago, Pete took a loan of $55,000. The loan was taken out for 10 years with an interest…

Q: ² - x ²² = y² dz ४x d²z Find the solution of xy' буду

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Q: Determine whether the vector spaces Ps(R) and M2,6 (R) are isomorphic.

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Q: a. 2 uxx = Иxy - 4uy azu J2u azu ди b. + +4 +3+u = 0 ?х у дуг ?х ?x2 ди c. k = 2 ,k < 0 ду 02u ?хг

A: Classification of the Partial Differential equations

Q: (c) Use Euler's Theorem and part (b) with a suitable value of p to find the remainder of 5103 when…

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Q: 3.27.2. Let X be a metric space with metric d; let ACX be nonempty. (a) Show that d(x, A) = 0 iff x…

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Q: Choose the function that has the graph below. Hint: Look at where the vertical asymptote(s) and…

A: Solution:-

Q: 4. Which of the following is false? A. The product of two rotations may be a translation. B. Every…

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Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) esch z. 8118

A: Squeeze theorem: If f(x)≤g(x)≤h(x) for all x and limx→af(x)=limx→ag(x)=L then limx→ah(x)=L…

Q: Q.1: Determine the roots of the Simultaneous nonlinear equations using Newton- Raphson method for…

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Q: 10. Prove that 7/2 TC/2- sin 0 cos (cos a cosec 8) de -0 2 (1-cos a).

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Q: se provide correct answer for b

A: Given,                   f(x, y, z)=xy2zconstraint to                  x2+y2+z2=64

Q: 1. Suppose n is an integer. Find all values of n such that 6n + 3 is divisible by 5. If there are…

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Q: Factor these two matrices into A = XAX-¹: 4 = 3 A [

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Q: Determine the values of r for which the given differential equation has solutions of the form y = t"…

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Q: Evaluate L-1{- [6] S -} + 169) (s - 9) (5².

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Q: 3.27.2. Let X be a metric space with metric d; let ACX be nonempty. (a) Show that d(x, A) = 0 iff x…

A: Let X be a metric space with metric d. Let , A ⊂ X be a non - empty. We need to show that , dx , A =…

Q: Given points P(4,2,-1), Q(2,-4,-1), T(4,3,4) forms the triangle. Find the unit vector that bisects…

A: We will first find the unit vectors along line QP &amp; QT. So that the resultant vector which is…

Q: Suppose h' is continuous x>0. IF x = 0 and h'(x) = 3√tan (2x)-1 it exists. i at Find h (0), 'F

A: For the solution of the problem follow the next step.

Q: In 3 Using 4-node Gaussian integration in approximating ³ x ex dx, which f(x) in the formula has…

A: Given: Let us consider the given, ∫1ln 3x ex dx and determine the approximation using 4-node…

Q: -1 5 -2 Consider the matrix A= 2 a) Obtain the eigenvectors (v₁, V2, V3) of A. b) Write a matrix P…

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Q: Example 10.25. Solve the initial value problem dy/dx=x-y², y(0) = 1 to find y(0.4) by Adam's method.…

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Q: Which one is a normal vector to the line which is perpendicular to the 8x - 3y = 9. OA (8,-3) OB.…

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Q: (-1 5-2) Consider the matrix A = 2 -5 5 2 a) Obtain the eigenvectors (V₁, V2, V3) of A. b) Write a…

A: Solve |A-λI|=0 for eigen values and [A-λI]v=0, where v is eigen vector.

Q: Let f be an arithmetical function (not necessarily multiplicative). Prove that there is a…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given the region enclosed by the curves x=cosecy, y=17π4, y=19π4, x=0 is revolved about the y-axis.

Q: 10. Prove that 7/2 75/2. sin 0 cos (cos a cosec 8) de 10 T 2 (1-cos a).

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Q: Find the exact ५००/२ Solution for y₁= 2-27

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Q: 8. Prove that the differential operator M: C² [a,b] → C[a,b] defined by d²u du Mu= 2+3u dx is a…

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Q: VIII. Suppose that f(x) is continuous everywhere and the graph of f'(x) is shown below. Do not…

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Q: (sinxy +xy cos xy) dx + x² cosx y d y = о

A: The solution is given as

Q: 3.7 The complete tripartite graph K, consists of three sets of vertices (of sizes r, s and 1), with…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not 2. lim (√x²-x-√x² + x)

A: limx→-∞x2-x-x2+x

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = e* sin(t), z =…

A: Curvature and radius of converges

Q: Find the Laplace Transformation of -3x y" +3y + 2y 4e when y (0) = 2, y' (0) = 4 28² +16s+30 OY (s)…

A: Given differential equation: y''+3y'+2y=4e-3x, y0=2 and y'0=4To find: Laplace transform of the…

Q: log (x+3) 2+1-1-cosh (cos-¹x) lim

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Q: A A particle is moving along a curve. Its x position is described by x = t² m while its y position…

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Q: [RX) S. If [²₁ f(x) dx = 12 and 24 X Enhanced Feedback Please try again. Remember, I'm f(x) dx. b +…

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Q: GGQ. VII. Consider the function f that satisfies the following: . f is continuous everywhere except…

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Q: fe²x+Inx² sin x² dx = +²√e²x cos x² dx

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Q: Let A = -5 0 74 0 2 64 20 4 4 3 5 4 4 Compute det(A) by hand by expanding in cofactors

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Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cos t) k…

A: The solution is given as

Q: Let f(x) be an irreducible cubic over Q with cyclic Galois group. Show that all roots of f(x) are…

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Q: a x In the experiment of tussing a fair coin is the randam variable giving 3 times the number of…

A: Given three fair coins are tossed. So PX = 0 = 18P(X = 1) = 38P(X = 2) = 38P(X = 3) = 18

Q: Prove that if n is an integer and n³ + 5 is odd, then n is even using a) A proof by contraposition.…

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Q: 1. Draw the circuit corresponding to the following expression. (Do not simplify your expression or…

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Q: line integral x³ dy), where y is t 3 X counter clockwise.

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Q: 6. Find the inverse Laplace transform of the function I(s) = (3² − a²) (as + b) (s² + a²) (s² + ß²)…

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