Find the equation of the tangent line of the function tan (xy²) = 2xy, a J absoleto 700 nu at x = π.

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A: The objective of the question is find the derivative .

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A: Solution of given question is written in below steps.

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A: Follow the procedure given below.

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Q: Question 2 S y dy Find √x+2 A ² (√x+2-5) (5√/y+2+y+24) + C 3 ℗ ²² (√5+2-5) (5√/y+2+y+21) + C B…

A: GIVEN

Q: If tan A = and tan B B = 1/1, calculate and simplify the following: tan (A - B) = [?]

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A: Volume = ∫ πy2dx here y = 16 -4x2 and limit from x 0 to 2

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Q: Consider 12-1 S= x-m+ 3x5 3x4+6x33x2 - 6x A B C + x-1 x + 1 x+m (A) 14/3 (B) 17/6 C) 5 6 —+ -dx.…

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Q: Find f 6x dx?a.x^2+C. b.2x^2+C c.x^2/3+C d.3x^2+C

A: The given integral,        ∫6x dx

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Q: Determine the area of region by y = x^2 + 4x and the y - axis

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A: Area is shown below÷

Q: 33x хе x³e³x dx S

A: This question is based on integral by parts.

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Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

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Q: Let f(x) = 3 cos 2x + sin² x. a) Show that f'(x) = -5 sin 2x. 3π b) In the interval 프 <x< 4 one…

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Q: find the values of λ for which the determinant is zero. 2 λ + 1 0 0 1 O(-1, 1, 1) O(-1, 1, 0) O(-1,…

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Q: Differentiate the following functions using Chain Rule: 1. y = (4x + 3)² 2. y = √5x-2 3. y = (6x-4)²…

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Q: y dy Find S y+2 O ²(√y+2−5) (5√/y+2−y+24) + C (√y+2−5) (5√/y+2+y+24) + C (√y+2-5) (5√/y+2+y+21) +C 3…

A: A detailed solution is given below.

Q: Read, analyze and solve for the following. Express your answers as decimals rounded off to two…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: 1. y = Ax² + Bex 2. y = C₁ ex cos3x + C₂ ex sin3x 3. y C₁e* + C₂e²x + x 4. Iny = C₁e* + С₂е¯* 5. x =…

A: As you have asked multiple questions so that I have answered first question as per the guidelines.

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Q: 3. fx² √9-x² dx

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Q: What is the derivative of the function r (x) 5 (9x²-2) (5x+7) (3x³-2x+2) 9x²-2 5 5x+7 3x³-2x+2 5…

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Q: Which of the following is or is not an improper integral? Clearly explain your choice. A. ₂ dx B.…

A: improper integral means whose limit at any point goes to infinite  here check for it. ∫1dx/(x-2) =…

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Q: 5. Answer the following questions. (a) Sketch a graph of f(x) = |2²-9 and find the points c such…

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