Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity diverges, enter DIVERGES.) 2 n- 1 dx = convergent divergent

Q: Find the volume by revolving the region of the curve xy = 6 from x = 2 to x = 4 about the x-axis.

A: Given xy=6        x=2 to x=4To find volume:

Q: Find a and b such that f(x) is continuous at x=1. [x – 2] + a x 1

A: A detailed solution is given below.

Q: Find the divergence of the vector field F. F(x, y, z) = In(9x2+ 6y² )i + 54xyj + In (6y? + 5z?)«…

A: To find the divergence of given vector field

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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Q: xArctanx - Invx² + 1 = y

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Q: 26 Select the correct answer. Which matrix can be multiplied to the left of a vector matrix to get a…

A: The given problem is solved below in detail.

Q: The position of a point at time t = 1 is (2, 4) and velocity of the point at time t is . Wha the…

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Q: Find a series solution about the ordinary point 0 of the differential equation y" + 8xy'-4y-0 O None…

A: The given differential equation is:y''+8xy'-4y=0We need to find a series solution about the…

Q: Arcsin(x/y) = 4x + 3y %3D

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Q: The integral X dx Vx2 – 4 3

A: To evaluate the given integral.∫12 xx2-43 dx

Q: The technique used to prove that x4 - 2x + 2/2tan-1 3 X + C 2. dx = - - x² + 2 is Long (Euclidean)…

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Q: 6. 19-x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) 2

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Q: dy find the dx +Ince 义 9 = sin In Cl+e)

A: The given problem is solved below in detail.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

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

Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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Q: 4ln(Arctan x) = 1- y

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Q: convert csc x/ cos x to sec^2 x/ tan x

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Q: Using Sandwich Theorem, the sequence 2 cos? n + 1 an = 4 - diverges converges to 0 converges to 2…

A: Use range of cos x which lies in -1 and 1

Q: Find the indefinite integral. (Use c for the constant of integration.) (2ti + j+ 6k) dt

A: Given query is to find the attached integral of the expression.

Q: Select one: 2s2 - 2s 6 S-3 O None of these 252 2s + 6 3 3s2 - 3s + 6 2 3s2 3s 6 S-2 Which of the…

A: Topic:- function  Note :- as per our guideline if more than one question uploaded than only first…

Q: Exercise 2. Find the following limits 3x +1 1) lim 2x +5 1-3x2 3x +1 2) lim X 2x +5 3) lim x- 2x+5

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Q: A statue 10 feet high is standing on a base 13 feet high. If an observer's eye is 5 feet above the…

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

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Q: A jet is flying through a wind that is blowing with a speed of 50 mi/h in the direction N 30° E (see…

A: --------------------------------------- Wind velocity: velocity: 50mphDirection: 30° with…

Q: Find the limit as x approaches c of the average rate of change of the following function from c to…

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Q: Determine whether the series is absolutely converger convergent or divergent. Please provide…

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Q: Given: a = 22, c= 24.1, zB = 6T C a A Solve the triangle. (Do not round until the final answer.…

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Q: Find the slope of the tangent line to polar curve r = 7 cos 0 at the point

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Q: need

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Q: Determine s) for $) = 31 + 212 1 s'() = 41 + 3 Os') = 41 + O s'() = 41 - %3D s'(t) = t+4t %3D

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Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

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Q: The integral dx – 4 3 1 Vx2

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Q: Determine whether the series is absolutely convergent, conditionally convergent or divergent. Please…

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Q: x-1 y = log x+1

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: Explanation of the answer is as follows

Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

A: Given:  xy3dx+(y+1)e-xdy=0xy3dx+(y+1)e-xdy=0(y+1)e-xdy=-xy3dxDividing equation on both sides by…

Q: Given a non-exact differential equation(x - sin?y)dy + sin y dx = 0. Find two integrating factors.

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Q: y=(1+2cot"x) 3 dy_ 8(1-2cot"x) dy 8(1+2cotx)° %3D dx 1-x dx 1+x? Op tion 3 Op tion 1 dy -8(1–2cot"…

A: Let's find.

Q: x-1 y = log. x+1

A: Topic:- application of derivatives

Q: Consider the following. u = 3i + 4j, v = -7i - j (a) Find u · v. -25 u v = 5- V 50 (b) Find the…

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

A: We have to find particular solution .

Q: 2) z= (1+t²)(3 - 2y); z' Ans: z' = -2(3t? + 3t + 1)

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: The integral dx Vx² – 4 3 -2

A: To evaluate the given integral

Q: Solving by variation of parameters y" – 3y' = x the general solution is: None of them c_1+c_2…

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Q: 3x+1 5) lim x+ 2x +5 2+Vx lim ²-3x 6) 7) lim 2-Vx

A: Limits

Q: y = log, x+1

A: Given: y=logx-1x+1