Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

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A: Solve for the value of y.

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Q: 1- Vx 6 Find the equation of the tangent and normal to the curve f(x) at the point 4, 5 1+ X

A: Given:     f(x) = 1 - √x / 1 + x  Points: ( 4 , -1/5 )

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A: We need to find directional derivative at p.

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Q: Given that Vf (7, -9) = 11 i – 6j, find the directional derivative of the function f at the point…

A: Given,           ∇f7,-9=11i-6j.            The function f at the point 7,-9 in the direction of…

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Q: 40-4V-V v? du

A: ∫40-4v-v2 dv∫44-4-4v-v2 dv∫44-4+4v+v2 dv∫44-22+2(2)v+v2 dv∫44-v+22 dv∫2112-v+22 dv

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Q: Q11. Obtain the general equation of the curve whose slope at any point is equal to y - 2x.

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Q: Simplify arccos2. no solution 30° 60°

A: Given query is to simplify the expression.

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A: topic - vectors

Q: Use an appropriate substitution to show that the value of the following definite integral has value…

A: SOLUTION-

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A: Here we have to find the equation of a plane.

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A: The given question has been solved in detail

Q: Find an equation of the plane through (-4, 3, –8) that is perpendicular to the line x – 2 = t, y +3…

A: Given line : x-2=t , y+3=2t ,  z=-tx-21=t , y+32=t , z-1=tx-21= y+32= z-0-1 comparing with standard…

Q: 9. cos(x-)

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Q: 12. A. If possible, give an example of 2 divergent sequences an and bn such that E(an + bn) has a…

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Q: Evaluate/Find the following integrals. 8x + 13 2. S -dx- 3 4x + 8x + x + 2 2

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Q: 7. [Geogebra Question] Let's use Geogebra to find the area of the region enclosed by the graphs of…

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Q: Evaluate (x² + In(y) +z )dV B = {(x, y, 2) | 0 <I< 1,1< y < 7,0 < z < 6} . Round your answer to two…

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Q: Use the elimination method to find all solutions of the system of equations. (Order your answers…

A: By using elimination method to find all solutions of the system of equations.2x2-y2=17x2+5y2=14

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A: answer is in next step

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Q: Evaluate the integral of x(x – 5)1²dx with limits from 5 to 6.

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Q: dy

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Q: 37. f(x) dx where f(x) sin x if 0 < x< T/2 cos x if T/2 <x< %3D

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Q: Let a = ci + jand b = 2i + 10j. Find c so that a and b are orthogona C = i

A: Given: a=ci+j b=2i+10j.

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Q: 27. x(2 + x') dx Jo

A: integration

Q: Find the Laplace Transform of the following functions 2as 4) f(t)=tsinh(at) Ans. F(s)= (s² –a²} |

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: Given f(x) = 1 –(5+ 10x) + (5 + 10x)² – 27 (5 + 10x)³ then f'(x) =, %3D - (5 + 10z) – ( 5 +…

A: f(x)=1-32(5+10x)+94(5+10x)2-278(5+10x)3 Then f'(x)=0-(32×10)+(94×2×5+10x×10)-(278×3×(5+10x)2×10)…

Q: 7 dx 5. S- xVx-4

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

Q: 2. Find the center of mass of the four particles having masses 2, 3, 3, and 4 kg and located at the…

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Q: Show complete solution

A: ∫01x1+xxdx23∫0132x1+xxdx23∫0132x1+xx12dx

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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