2. Set up triple integrals in cylindrical coordinates that compute the volumes of the following regions (do not evaluate the integrals): a) the region A bounded by the sphere z² + y? + z? x² + y° + z= 0, 12 and the paraboloid b) the region B in the first octant bounded by the surfaces z = r² and r² +y? + 1, and c) the region C inside both spheres r² + y? + (2 - 2)² = 16 and r² +y² +z? = 16.

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Q: dx X +T 2. 3.

A: ∫x32x3+π = -3(lnx+3π6x+π3-lnx-3π6x+π3)-2(arctan2π56x+3 ππ+arctan2π56x-3 ππ)-4arctan(xπ6)6π6

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Q: 1. e (3xy-x)dx+e dy 0; when x = 0, y = -1 4 Ans. y =--e* 3 3

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Q: OM 3. In the differential equation (y – x - 4x-1kdy + 2y(x+ y+2kdx = 0,

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Q: 3. Evaluate the following INDEFINTE integrals. (a) / (b) / va dy y dy (c) dy

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for yo...

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A: This is  a problem of vector. By dissolving vector in x and y parts we will convert it into componen...

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A: for (a) - critical values is +3 and -3  for (b) - the relative maximum point is x = -3 and relative ...

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A: Answer is given below. C option is correct  

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A: Use integration by parts method.

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Q: Зх-1 -dx 2 x+1

A: Given query is to find the integral.

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Q: () () Consider the following two series A = E n=1 and B = Which of the following statements is TRUE?...

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Q: a Let A = b be 2 x 2 matrix such that d 3A' +2 Find A. 1

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A: x=3t1y=2-t1z=-1+t1andx=1+4t2y=-2+t2z=-3-3t23t1=1+4t2  ...(1)2-t1=-2+t2 4-t1=t2  ...(2)-1+t1=-3-3t22+...

Q: Use an addition or subtraction formula to find the exact value. 1. sin15° 2. cos 12 3. tan 75°

A: 1.Sin15o sin(15°)=sin(45°-30°)              =sin(45°)cos(30°)-cos(45°)sin(30°)   {sin(x-y)=sin(x)cos...

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A: The given function is f(x)=x7x.

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A: According to question,Given function,y1 = 2 cos x,y2 = cos xy3 =0.5 cos x0≤x≤2π

Q: The numerical value of the improper integral (tx) 3 dx is equal to (x*+1) 2 - 00

A: Please see the answer below.

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A: Given curve: y=4cos3x-3cosx To find: The values of x when y is maximum and minimum i.e. critical poi...

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Q: Direction of opening: Zeros: y-intercept: Vertex: Axis of Symmetry: Max or Min Value:

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A: Given that,

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Q: 2. Show that, in the region D: 0 < x<1, 0 <y< x², the following double integral 1 dA =- In(2) x5 + 1...

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Q: (d) 5 (-1)" Vn +1 n=1 1 (e) Σ- nylnn n=2 n (f) 2 In Зп + 1 n=1

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A: Volume , V = ∫∫∫dV = ∫∫∫R dz dy dx

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A: integrate

Q: Scanned With Camca Find the maximum of f(x) = et

A: This question can be solved using the concept of maxima and minima.