Differentiate the function. f(x) = x²(x + 8) f'(x) = x³ (x + 8) 3 X

Q: (2) Z/(5) =........ (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find out integer

Q: An ocean liner is sailing north at a rate of 13 miles per hour. The ocean current is flowing N-10°-W…

A: In this question we have to find the velocity of the boat relative to land and what direction is the…

Q: 3 Evaluate: 2₁ (4x²yz - 2 ) dz dy dx 4

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Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given problem is :

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

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Q: 5x 3 Evaluate: fffdz dy dx 2

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Q: A particle is moving along the curve whose position vector is given as R(t) = (t)i + ( În (cost)) j…

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Q: Consider the parametric curve: x = 5t² y = 2et Which integral gives the arc length of the curve over…

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Q: зи Evaluate the integral: So So So u s2 +u2 ds du dt

A: Given: I=∫02∫0t∫03uus2+u2dsdudt   As we know the common integral. ∫11+x2dx=tan-1x+C

Q: Evaluate: ƒ³, ƒ²₁ √√₁²[z³(x + y)³] dz dy dx -3

A: Given :∫-33∫-12∫01z3x+y3dzdydx

Q: f(x)=2x+1(3x-1)

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Q: Find the area of the region bounded by the curves y = 1 (x+1)21 2 y = 4 and

A: Please refer to the image below

Q: Evaluate: 1+ 2y dy dx •x x2

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Q: -3 (x² - y²)²] Evaluate: ₁²² x+y du dt

A: Given

Q: S¹₁₁ S1+₂x² x + 2y dy dx ·12x²

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Q: What will be the orientation of the curve of the graph of the function f(x) = on (-3,0)? A.…

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Q: elaborate pls, i could not understand the flow of the solution

A: We have to elaborate the solution.

Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: 1 (x² - y²)² x+y valuate: ²₁₁² dx dy

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Q: 2x-1 Q7. Find the convergence interval and radius of the series : 2 (-1)" . Σ(-) 2n-1 n=1

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Q: Evaluate the integral: ft² ns te" du ds dt

A: Let's evaluate given integral.

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ y = 4 and the x-axis using vertical…

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Q: -3 ³₁₂₁(4x²y - z³) dz dy dx

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Q: Q9. If W = f(u)=u³ +sin ¹u+lnu, and u= ax +by, where a, and b are constants, show that aw Əw b oy Əx

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Q: (1 + y²)dx + (x²y + y + 2xy)dy = 0 Ox+2y² (1+x)² = c O 2x+y2(1+y)2= O 2x+y?(1+x)2=c y² x)² Ox+y²…

A: Solving by seperation of variables

Q: 3 Evaluate: ³₁²₁ ¹²[z³(x + y)³] dz dy dx -4 1

A: Given

Q: valuate: xy² dx dy

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Q: 4. The position of a particle moving along a horizontal path is given by s(t) = t³ - 4t² - 3t+8,…

A: This is a problem related to differentiation of the function. Based on the general formula and…

Q: 11.Doe = 8. Find the slope of the secant line. f(x) x-8 3x+4 X1 = 2, X₂ = 0

A: Here we have to find the slope of a secant line.

Q: Find a number in [0, 1] such that the difference of one third the number from its cube is minimized.…

A: Let the number be x. Let f(x)= x³-x/3 So, f'(x)= 3x²-1/3

Q: (5) If f(x) =........, then f(x) is reducible in Z5 [x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x²…

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Q: 7. s sec² cot √sec4-2 sec²-3 dø

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Q: 5.) I. -2 -3 -6 2 Simplify. Write "undefined -4 6 0 +

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Q: Q7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

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Q: What are the first 5 terms of the sequence represented by a=2n-3a n "n-1, where a₁ = 4₂

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Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Given that      Region R : 0≤x≤1 , 0≤y≤1-x2 , 0≤z≤4-x2+y2    Now, we take…

Q: Use the table of integrals to evaluate the integral. 2 5x³√4x² - x4 dx

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Q: Find the point on the line y = 8x closest to the point (1,0). (Use symbolic notation and fractions…

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Q: Evaluate: xy² dx dy S

A: Given: ∫04∫0yxy2dxdy

Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√s s4

A: A detailed solution is given below.

Q: The value of A. -√4+C 4x B. +C √4-2 C. D. 4√4-x² 4√4-x² S ₁4- +C +C dx (4- x²)1.5

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Q: Q8. Solve the following D.E to find y as a function of x : dy dx y sin 2x 3y² cos2x

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Q: y"" - 4y" + 3y = 0

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Q: What is the equation of the tangent line to the curve y = at point (0, 0)? O none of the choices O y…

A: Given :      y = 3√x    Point : (0 ,0)

Q: What will be the orientation of the curve of the graph of the function f(x) = 3 on (-3,0)? z² z+3 O…

A: Given the function  f(x) = x2x+3 on -3, 0.

Q: S77/2 Su² sin (=) dt du Evaluate the integral: f/2.

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Q: Let f : R 7−→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find f^(−1)(x).

A: Let f:R→R be defined by f(x) = 2 - 5x.

Q: 5. I. Evaluate each determinant. -2 -1 4 2 5

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Q: s s² s² sln teu du ds dt

A: We have to solve multiple integration.