O Determine if the line and plane intersect. If so, state the solution. T: -2x+6y + 4z_4=0 L: [x, y, z]= [5, -1, 4]+t[1, -2, 3]

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A: It

Q: Evaluate the indefinite integral du =

A: The solution of the integral is given below:

Q: √4x²(x³-5) dx = x³ (x¹2 - 25x² + 250x6 - 1250x³ +6250) + c O 16(x³ - 5)4 + c O(³-5)5+c O (2³-5) 5+ c

A: See the details solution in below

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A: We have to solve given Questions.

Q: P1: Calculate the area bounded by the curves: C. y e* and x - 2y + 5 = 0, and y-axis.

A: To calculate the area bounded by the following curves.y=e-x and x-2y+5=0, and y‐axis.

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A: The inverse laplace tranform L-11s-73

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Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: 1) The hyperbolas 6² x ² - a²y² = a) xyy" + x(y²) ²³²- yy²=0 b) xyy" - x (y² 7² - y₁² = c) xyy" - x…

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Q: Find two numbers whose sum is "a", if the product of one to the square of the other is to be a…

A: sum of two numbers is 'a', the product of one to the square of the other is to be maximum

Q: let A be a bounded. Sup A non. n-empty set in R show that is a limit point of A.

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Q: The midpoint of AB is at (0, 0). If A = (-5, 4), find B. B is: (

A: Given :A=-5, 4Mid Point of AB=0,0

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A: Let's solve diffrential equation by using laplace transform.

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A: We know  Function differentiable if it is continuous through out its domain   At sharp/corner points…

Q: f(x) = 3x² - 5x+21

A: SOLUTION-

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Q: a. [8t7dt dx b. S sin x tanx C. d. S [ 26* dx 3d8 √8

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Q: (2x-1) dx 1 2x²³²-x²-27x +36

A: …

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A: Given :laaalaaal=2a+ll-a2

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A: To find interval of convergence of ∑n=2∞ (x−2)nln⁡(5n) Let an = ∑n=2∞ (x−2)nln⁡(5n) Therefore, an+1…

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A: Given :

Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: Find the area of the region described. 4 1 The region bounded by y = and y = - 1-x 2

A: To find the area bounded by the curves y=43&y=11-x2. The region bounded by the curves is:

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Q: 1. 2. 3. The degree of the differential equation (1²³²)² + (¹x² A. 3 C. 1 B. 2 D. not defined The…

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Q: Q1) L-1 s(s a) cosht -1 b) 1-cosht c) (cosh2t - 1) d) (1 - cosh2t)

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 8, f'(9) =…

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