the surface generated by revolving about the y-axis the part of the Find the area of 2 curve y = x between x=0 and x=1.

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Q: Let <0,4,27 < 3, 0 , 1) What is the having the same direction B- ZA + c ? unit vector as

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Q: Find the limit of the sequence: 4n? + 2n + 3 An 4n2 + 6n + 2

A: limn→∞ 4n2+2n+34n2+6n+2=limn→∞ 4+2n+3n24+6n+2n2=limn→∞ 4+2n+3n2limn→∞ 4+6n+2n2=44=1

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A: We have to check continuity of the function

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Q: In R?, using vectors and angle between vectors, verify that the points P (13, –1 Q(-9,3) and R (-3,…

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Q: x2 – 25 dx 7) S-

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Q: Find the mass of the sphere x2 + y2 + z2 = a2 where the density at any point is two times the…

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Q: a) Compute the area of the shaded region by "counting" the squares on the grid in the given region.…

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Q: For each of the following series determine if the series converg for series convergence or…

A: Given

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A: f(x)=x3-16x+2    ;  [0,4]

Q: 2 - y 3. Consider the lines defined by the equations &3 : x – 1= 3 – z and l4(s) = (1 – 2s, 4s, 1 +…

A: Given problem:-

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Q: Verify that the two planes are parallel. --x + 6y + 2z = 7 *+ 3y + z = 8 Find the normal vector, n,,…

A: The normal vector to the plane ax+by+cz=d is given by n=a,b,c

Q: 3- x 3) dx → S2xe* dx

A: To evaluate the given integrals.

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Q: -1 8 - 2 Use this procedure to find the inverse of A =| -6 49 -4 34 -5

A: We can solve this as follows:

Q: Solve the following and show the complete solution. Find D,f at P: f(x,y) = sin(8x – 5y); P(5,8)); u…

A: Given,            fx,y=sin8x-5y ; P5,8 ; u=35i-45jTo find : The directional derivative, Duf at P.

Q: Determine if the given sequence converges or diverges. If it converges, what is its limit? 5 + 3n3…

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Q: /3x+10 4 Evaluate lim x- 2- x2- 4x +4 А. 1 В. 3/8 D. -00 E. None of these C.0 B O D E O A

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Q: What is the contour map of the function using the given values of k? t(x, y) 1 1 1 1 x² + y? k = 0,…

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Q: Find f'"'(x), the third derivative of f, and f (x), the fourth derivative of f. f(x) = 7x* + 2x³ +…

A: In the original solution it had been shown that:  f4x=ddxf'''x=ddx168x+12=1681+0=168

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D %3D v (0, 6) %3D b =

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Q: Determine the of : In (xy²) = x y dx

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Q: Question A vertical cylinder is leaking water at a rate of 8 m³/sec. If the cylinder has a height of…

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A: Solution is given below:

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 %3! +3y +z 8 Find the normal vector, n,,…

A: We have to check whether the given plans are parallel or not or we have to find distance between the…

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Q: 4. S ( 12 x³ + 15 x - 20 ) dx 5. S 10 x2/5 dx 6. § 3 ³V x8 dx 7. S ( 8 + 2 dx x3 x4. 8. S ( 2x³ -…

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Q: xe* хе dx. J (x + 1)2

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Q: Find the vector component of v = (4, – 1, 7) along b = (4, 4, -7) and the vector component of v…

A: Given,            V= &lt;4,-1,7&gt;            b =&lt; 4,4,-7 &gt;

Q: Problem: 2 a. Find all the asymptotes of the following functions 4x* + 4x3 + 12x2 + 6x – 24 6x* + 8x…

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Q: Find the area of the shaded region. Edit = Vco r = COs 20 r = 2 cos 0 NOTE: Enter the exact answer.…

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Q: Evaluate lim v9x² – 5x + 3x x - 00

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) = V…

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Q: Use limits to determine all the linear asymptotes of 3x2 – 5 if a1. a² + 2x – 3'

A: Let's find.

Q: Find u · v, u · u, ||v||². (u - v)v, and u · (3v). u = (3, 12), v = (-2, 3) (a) u. v (b) u.u (c)…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: 1. Given z, = 5 cos 377 +i sin 37 and z2= 37 +i sin 2 find z,z2 where 0se< 2x. cos 2 2 37 +i sin 2…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 -*+ 3y + z = 5 Find the normal vector, n,,…

A: