hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht: Solve the quadratic equation in y for y in terms of x, and express y as two functions of x.

Q: (ii) Evaluate L-¹ {,2²9}. [2

A: Sol:- L-12s2+9 =L-123·3s2+32

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Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). x³y"" + 6x²y" + 4xy' - 4y = 0

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Q: Question 20 Given the equation -4x² + 8x - 4y² – 56y - 4z² + 32z = -312 - a) Show that the given…

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Q: E (TL) ARP2 ARP3 ARP1 ARP2 ARP3 ARP4 Notes: • You are allowed to use your triangles to produce…

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Q: Use undetermined coefficients to solve the differential equation y"" -y=e¹- x + 16.

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Q: Find the three areas of the region bounded by y= 2x²+10 , y=4x+1 and the lines x=-2 and x=5.

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Q: What is the equation of the asymptotes of the hyperbola defined by x² - 4y² + 4x + 40y - 92 = 0

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Q: (b) Sketch the polar curve r= √cos 20 and r=2 cose. Then find the area of the region that is outside…

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Q: 1- 4x²y" + (4x² + 1) y = 0 a. Show that the equation has a regular singular point at x = 0. b.…

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Q: Question 5 Find s [c 0.84 3 -i cos 3z -0.48 3i 0.84 3i -0.84 dz along the contour from 1 to .

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Q: 510 120 + 128 64 Q6/ 96 6528 186 456 18 128 16 A. The region in the first quadrant bounded above by…

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Q: 1. Show that if f: [a,b] → R and a < xo <b, then f'(xo) exists if and only if D f(x) = Dƒ(x) € R.

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Q: 0.80 0.10 0.10 Find the stationary matrix for the transition matrix P = 0.15 0.80 0.05 0.20 0.70…

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Q: (a) Determine the eigenvalues in terms of a. (b) Find the critical value or values of a where the…

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Q: 40. The cubic x³ - 2x² - x + 1 has three real roots; one is negative. a. Find a rearrangement that…

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Q: 1. a) Obtain a second-degree polynomial approximation to f(x) = (1+x)¹/2, using Taylor series…

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Q: what is the terminal velocity? 5 meters/second How long before the object reaches 90% of terminal…

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Q: Question 20 Given the equation -4x² + 8x - 4y² - 56y - 4z² + 32z = -312 a) Show that the given…

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Q: Altitude (m) Temperature (°F) Plane Altitude and Outside Temperature 0 500 1000 1500 2000 2500 3000…

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Q: Solve the following (given as the augmented matrix): 31 -4 1 -5 5 1 10 -2 3 20 7]

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Q: 11. Find the F in the surface S integration ffrnd where n is the normal unit vector to the S F=xi+zk…

A: Given F=xi+zkS : 2x+y-2z=6  where x≥0, y≥0, z≤0

Q: True or False: You cannot use chain rule of  integration when working with exponential function.…

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Q: Given 3 y₁ = x²³₁ (0,00) is soln to x²y²-6y=0 find y₂ and show linea independence.

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Q: Solve the following: 1. 240,000 x 0.006 2. 3. 460,000+ 0.0002 0.00048 + 6,000

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Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). ry" +6x²y" + 4xy' - 4y = 0

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Q: 2. Finite subsets of Rd are closed.

A: Here we have to prove that any finite subset of ℝd is closed. Here we can use that union of close…