Abe 21. ff sin²x dA, D D is bounded by y = cos x, 0≤x≤ π/2, y = 0, x = 0

Q: Prove by induction that Σ₁(5¹ + 4) = 1/(5¹+¹ + 16n − 5) -

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Q: The formula for the quadratic function y = f(x) such that: f(0) = -35, f(-1) = -36 and f(1) = -32 is

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Q: Find the general solution of the given system. =( X(t) = X' 10-20 8-18

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Q: ) Solve for the general solution of the equation: 2x’’+ 200x = 0 B) Solve for the particular…

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Q: 0 -8 -4 -4 (a) The eigenvalues of A are λ = 3 and λ = -4. Find a basis for the eigenspace E3 of A…

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Q: Use triple integral to find the volume of a solid

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Q: Fit y = a e Xi 1 2 3 4 LC 5 6 7 Yi 1.1 2.2 3.2 5.4 6.1 Bx using a natural logarithm transformation…

A: Xi Yi 1 1.1 2 2.2 3 3.2 4 5.4 5 6.1 6 10.1 7 15.7 The curve to be fitted is…

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Q: could you also do part b for this and on a piece of paper preferably.

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Q: B.X2 = 4x₁ + 6x₂ + 4x3, X'3 = 5x₁ +4x2 +5x3 tion in matrix form? ...

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Q: Using the Residue Theorem, show that dx S 100 (X² + 4) ² ㅍ 16

A: By using the residue theorem to show the  real integral ∫-∞∞1(4+x2)2dx=π16

Q: 9. Find the derivative of the function. Simplify. f(x)= In

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Q: Prove by induction that the following statement is true for all positive integers. 2³n— 1 is…

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Q: 8. Explain how to calculate 29 x 20 mentally by using 30 x 20. Write an equation that uses…

A: (a + b)×c = ac + bc

Q: 1. Show that Σμύ - Σύ =

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Q: 2. (Hopf Bifurcation.) Consider the system x' =ax - y = x(x² + y²) - y' = x + ay − y(x² + y²), where…

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Q: x14 + + 214 4. Sketch completely and identify the surface represented: y =1

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Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

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Q: Sketch the region of integration and change the order of integration. 5 √25 - y² L'₁ PX, 1 -5 f(x,…

A: We have to sketch the region of integration and change the order of integration.

Q: (a) Find the best approximation to ✅ by a vector of W. (b) Write as the sum of a vector in W and a…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

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Q: Q.1) A horizontal shift 8 units to the left. A vertical shift 12 units down. A reflection over the…

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Q: 1. Let S₁ and S2 be collections of sets. Prove the following a = SESIUS2 • (U₁) U(US) - U S…

A: 1. (a) Let any x∈∪S∈S1S∪∪S∈S2S This implies ⇒either  x∈∪S∈S1S  or  x∈∪S∈S2S or  both. This again…

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Q: Exercise 10.3.14: Prove that for any two subsets A, B C R", we have m* (AUB) ≤ m* (A) +m* (B).

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Q: For the surface given by z = x4 f(x, y) = x² − 6x² which of the following is true. Select one: a. b.…

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Q: f090f = (456) (1984) (275) (36) (654) २३ 4.5 6 974.3 । २ 789 658

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Q: lím [√x4 + 8x² + 3-√√x² + x² x →∞

A: limx→∞ x4+8x2+3-x4+x2 To Find: Evaluate the above limit.

Q: for part b could you explain in more detail how f is involved. Thank you

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Q: Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. A= 12 5 -3 6 12 0 26…

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Q: 8. Use (a) parametrization; (b) Stokes' Theorem to compute fF.dr for the vector field (x² + z)i +…

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Q: we have found that A has two eigenvalues, The eigenvalue λ = 6 was found by considering the set of…

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Q: determine orthogonal bases for rowspace(A) and colspace(A) 15 24 12. A = 3 3 42 51

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Q: (1) (F, ñ) dS, (2)F(x, y, z) = 27 + 5j + 3k e Sé x² + y² (4) x² + y² = 1, (3) (5) (ni, k) <0.

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Q: can you explain part (c) in more clear/ simple steps? thank you

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Q: oblem 7.3: Using two methods to find the PS of (x' = 4x - 3y y' = 3x + 4y x(0) = 1 y(0) = 2

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Q: 3.For the vector field F = 2(x + y) - 9 2x² + 2xy, › evaluate fF.ds where S is the upper hemisphere…

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Q: 2.::m dy = sin 5x dx we obtain y = -cos 5x + c. Em dy = (x + 1)2 dx we obtain y = (x + 1)³ + c. om…

A: The given differential equation is a separable differential equation.

Q: -) a) Using the extended CIF compute: (Justify your steps! (dz 121=2 (2=5 dz iii) 12/1=3 (2+1) 812…

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Q: R is the region bounded by the given curves. R: y = x², x = 0, x = 1, x-axis Find I R IR (Assume a…

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Q: 2. Cylindrical Projection To map the entire world using the cylindrical projection, the cylinder…

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Q: H independent and whether the set spans R³. Determine whether the set 1 -2 2 -1 6 2 is a basis for…

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