2. The curve determined by the equation y2 = x²(x + 3) intersects itself, forming a loop. Find the area enclosed by this loop.

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Q: Answer Q-3

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A: This is called as the Chinese Remainder Theorem

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A: Put x= r cos and  y=r sin .

Q: 1

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Q: |||| = u = = Find the norm of x and the unit vector u in the direction of x if 1 -A 4 = -5 18 ||

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Q: Find the maximum value of f(x1, x2, x3) = 6x₁ + 7x₂ + 2x3 subject to the following constraints. S x₁…

A: subjected to constrain

Q: for a fixed n>1 Show that all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

A: To Proof: For a fixed n>1 , all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

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Q: Problem #10: Find the flux of F(x, y, z) = yi — xj + 7k across S, where S is the helicoid with…

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A: Here we have to find the p(x) and q(x) that are basis of given vector space.

Q: 14. Discuss the differentiability at x = 0 of the function 1 x sin -, x = 0, x f: x→ 0, x = 0.

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Q: Let f: R → R³ be defined by f(x) = (8x, –7x, –9x). Is ƒ a linear transformation? f(x + y) = f(x) +…

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Q: Solve non-homogeneous equation: y" - 9y=-xcos3x

A: We have to solve non-homogeneous equation:y" - 9y = -xcos3x

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Q: 19. As in Exercise 18, calculate A¹0x for 1 2-1 05-2 6-2 A = 0 and x = 2 4]. 7

A: