Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 1/x°, y = 0, z = 3, x = 8; about the y-axis.

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: (x + y) dx dy dz =? Select one: 9. O 1 O 5 None of them

A: Topic = Integration

Q: 4 Find f(x) dx if if x< 2 f(x) if x 2 2.

A: To evaluate the given integral

Q: The polar equation of the curve is expressed as r = 2sine + 2cose. area bounded by the curve.

A: To find the area.

Q: 5. (1 + e*/") + e*/ dy

A: Solution

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

A: Use limit concept

Q: 16X

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

Q: Given the following differential equation (E): y" + 2y' + 5y = 0. The solution of (E) is: O None of…

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Q: An isotope of the element erbium has a half-life of approximately 13 hours. Initially there are 24…

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Q: Q2. An object is kept at a distance of 20 cm from a concave mirror. A real mage is formed at 20 cm…

A: Topic:- algebra

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Explanation of the answer is as follows

Q: (c) Find marginal profit at q = 500. 10 Explain what it predicts. The total profit will increase by…

A: Apologies for the inconvenience.   #c) We have found that marginal profit at q=500 is 10.  It means…

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Q: Using decomposition into partial fractions, 4x2 + 2 -dx x(x² + 2) is equal to In|x (x² + 2)| + C…

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Q: fintthe XP COS ५: टे. 8 e

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Q: The integral X dx Vx2 – 4 3

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

Q: Using appropriate substitution, S [sec³ (2x) – 2] tan(2x) dx is equal to

A: integration

Q: can you say about the series a, in each of the following cases? |an+1 lim n- c0 (a) an absolutely…

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Q: Differentiate Зх — 6 y = csc 5x2 + 9 A. Зх — 6 Зх — 6 - y' = cot csc 5x2 + 9 5x² + 9 ) В. Зх — 6 Зх…

A: Differentiation

Q: EXERCISES Solve the following differential cquations 1. =-sec(xy) Ans. sin x = +C dx 2x2 x +y Ans.…

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Solve the equation xydx - (x + 2)dy = 0

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Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: convergent or divergent. Please provide detailed solution. a) : E 10" n=1 (n + 1) 52n + 1 00 -5n 2n…

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

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Q: Given the area in the first quadrant bounded by x^2 = 8y, the line y - 2 = 0 and the y-axis. What is…

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Q: Find the Area bounded by the given curves. 1. у %3 х2, у32х+3 2. х2 - у -1, х3у -3 3. у 3 х2, у-2-х2

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

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Q: Using appropriate substitution, [sec (2x) – 1] tan(2x) dx is equal to

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Q: dx Which of the following functions satisfy the differential equation = x? dy O x= e o y= e* O x=y O…

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Q: 3 y = Vx and y = x³

A: We have to find the area by using definite integral

Q: 8. Sketch a graph (different for each) that satisfies the given conditions: a) f'(x) 0 if x -2 (x…

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Q: dx J1- ² 2x + x°

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Q: Change from spherical coordinates to rectangular coordinates $ = 6. O z2= 3(x² + y²) O z2= 3(x²…

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Q: Find the general solution of the differential equation dx = xin (xy)

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Q: Determine whether F(x, y) = 3xi + 7yj is a conservative vector field. find a potential function for…

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Q: evail hupisuoɔ əui 8u the partial fraction decomposition for 5x² – 3 - f(x) (x³ – 4x²)(x² – 3x +…

A: We have to find out partial fraction

Q: Stan@ -1}de

A: ∫ tanθ dθ = -lncosθ+C ∫sec2θ dθ = tan θ +C.

Q: [a csc ()- y] do + ædy = 0 CSC O y= x cos(In z) + C O y=D cos (In a + C) O In + cos(E)= C O Ino COS

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: Find r'(t), r(t,), and r'(t,) for the given value of to r(t) = (e', e²9), to = 0 r'(t) = r(t,) =…

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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: 1/5 2n'5 3) Use the Limit Comparison Test to determine whether the series V5n + 7n+7 n=1 is…

A: Given problem:-

Q: Find the right-hand Riemann Sum, with three sub-intervals indicated by the table. Hours 7. 8.…

A: We have to find the right hand Reimann Sum.

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

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Q: Consider the differential equation (x- 1)y" + y' = 0. By using power series so- lution about the…

A: Please see the below picture for detailed solution.

Q: The cylindrical coordinates of the point with rectangular coordinates (-V2, -v2, v2) are (v2, , V2).…

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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: Use the graph of y fx) shown at right to find the domain of f. 345) (-63) 9,3) The domain of fisO…

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Q: y = sinx dy V1+x? sin dy V1+x sinx+x x+x (sin" x)' Jī- dx (sin" x) Vi+x² dx Op tion 2 Option 1 V1-x…

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Q: The following sequence (7532h n! an = e O diverges converges to e converges to 0 converges to 1

A: Given problem:-