cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

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Q: What is f'(x) given the integral function •5x+1 f(x) = 5x+¹ cos(e") du? ○ f'(x) = 5 cos (es) o f'(x)…

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Q: 2π π +][im [[(sinx + cosy)dxdy πο 5.

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Q: 4. 4 1 [x²ydxdy 20

A: The objective of the question is evaluate the double definite integral.

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Q: 3 5. S (t + ²1) ²³ dt t

A: To evaluate the integral.

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A: I am attaching image so that you understand each and every step.

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Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: 03/ A. For the following function f(x). Find: ji. iii. m=? 1-4X m -UX.=-u P(1,-1) f(x)=x-2x² The…

A: See this solution in below

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Q: 2A)Matrix A = 12 2₁ B = B = [₁ ²2₁ find AB. -21

A: Note:- Please repost part B because unable to understand  right side of differential equation…

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Q: Exercises L- If H B =). 33" 3 14. BB+A-SI-D E A-

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Q: 6. f(8x³ - 6x² + 12x −9)dx

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Q: d) Find the slope of the parametric equations x=2+3sin and y=0-cose at 0=

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Q: x² + ax − 2bx - 2ab-x³-2ax² - 2bx² dx x² + ax³ - 2bx³ - 2abx²

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Q: Find local maximum local mainimum Critical points Increasing decreaing interval

A: The solution is given below

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Q: 13. 2ny(8- y³/2) dy A) 4² (14 — y³/²) + C 7 2my 7 (14-y3/2) + C C) B) T² (14+y³/2) + C 7 D) 4²…

A: 13. The given integration is: ∫2πy8-y32dy To evaluate the given integral.

Q: 4. What is the length of the latus rectum of the ellipse whose equation is (x-3)² + 2 = 1. 25 16

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Q: Q5/ Find the area of the region enclosed by the curve y² - 4x = 4 and the line 4x - y = 16. 3,6 16…

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Q: 4. √ (4x²–5x+6) dx

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Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…